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Задания, страница 149 - гдз по геометрии 11 класс учебник Смирнов, Туяков
Авторы: Смирнов В. А., Туяков Е. А.
Тип: Учебник
Издательство: Мектеп
Год издания: 2019 - 2026
Популярные ГДЗ в 11 классе
Глава V. Объемы тел. Параграф 26. Объемы пирамиды и усеченной пирамиды - страница 149.
App\Models\Task {#1003 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1146625 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "149" "field_page_end" => null "field_url" => "/11-klass/geometrija/mektep-smirnov-uchebnik-dva-2019/samost-149" "field_display_title" => "Задания" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1008 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1006 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1017 #items: array:1 [ 0 => App\Models\Branch {#1016 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1145842 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы тел" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1021 #items: array:1 [ 0 => App\Models\Term {#1018 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "133" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1029 #items: array:1 [ 0 => App\Models\Book {#1028 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4310 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1033 #items: array:1 [ 0 => App\Models\Term {#1030 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6477 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #original: array:10 [ "id" => 6477 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ 0 => App\Models\Term {#1032 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5460 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1034 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6996 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1031 #items: array:2 [ 0 => App\Models\Term {#1046 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5801 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5801 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7017 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7017 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\Term {#1045 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Естественно-математического направление" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1266" "field_priority" => "6" "field_default_folder" => "/geometrija_11/smirnov-2-u19/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/geometrija_11/smirnov-2-u19/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_11/smirnov-2-u19/covers/cover1.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_url" => "/11-klass/geometrija/mektep-smirnov-uchebnik-dva-2019" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 382 "subject" => 543 "class_subject" => 393 ] ] #original: array:50 [ "id" => 4310 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1033} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1031} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1041} "field_country" => Illuminate\Database\Eloquent\Collection {#1042} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1040} "field_umk" => Illuminate\Database\Eloquent\Collection {#1036} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1049} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1050} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1051} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1052} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Естественно-математического направление" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1266" "field_priority" => "6" "field_default_folder" => "/geometrija_11/smirnov-2-u19/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/geometrija_11/smirnov-2-u19/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_11/smirnov-2-u19/covers/cover1.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1053} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1054} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1055} "field_url" => "/11-klass/geometrija/mektep-smirnov-uchebnik-dva-2019" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1056} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 382 "subject" => 543 "class_subject" => 393 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1019 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1145842 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы тел" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1021} "field_page_start" => "133" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1029} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1019} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:2 [ 0 => App\Models\Branch {#1086 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1145842 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы тел" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Term {#1018} ] #escapeWhenCastingToString: false } "field_page_start" => "133" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Book {#1028} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1145842 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы тел" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1087} "field_page_start" => "133" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1088} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1089} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1090 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1145846 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы пирамиды и усеченной пирамиды" "field_branch_order" => "26" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1091 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1093 #items: array:1 [ 0 => App\Models\Book {#1028} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Branch {#1016} ] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1145846 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Объемы пирамиды и усеченной пирамиды" "field_branch_order" => "26" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1094} "field_page_start" => "147" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "book" => Illuminate\Database\Eloquent\Collection {#1093} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1092} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1009 #items: array:2 [ 0 => App\Models\Element {#1069 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1390802 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Edition {#1059 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5035 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1034} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1022 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1024 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5035 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1058} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1022} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1024} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1146625" "type" => "task" ] "text" => "<p>Выведите формулу объема правильной:</p><p><strong>а) треугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.</strong></p><p>$V = \frac{\sqrt{3}}{12} a^2 h$</p><p><strong>б) шестиугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.</strong></p><p>$V = \frac{\sqrt{3}}{2} a^2 h$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "149-1.jpg" "alt" => null "width" => "1802" "height" => 226 "path" => "/media/geometrija_11/smirnov-2-u19/0-samost/149-1.webp" ] ] ] #original: array:7 [ "id" => 1390802 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1060} "task" => array:2 [ "refs" => "1146625" "type" => "task" ] "text" => "<p>Выведите формулу объема правильной:</p><p><strong>а) треугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.</strong></p><p>$V = \frac{\sqrt{3}}{12} a^2 h$</p><p><strong>б) шестиугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.</strong></p><p>$V = \frac{\sqrt{3}}{2} a^2 h$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "149-1.jpg" "alt" => null "width" => "1802" "height" => 226 "path" => "/media/geometrija_11/smirnov-2-u19/0-samost/149-1.webp" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1067 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1566106 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1023 #items: array:1 [ 0 => App\Models\Edition {#1020 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5689 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1014 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7012 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "gemini 2.5 pro" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1012 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5689 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1077} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1079} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1012} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1076} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1146625" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Правильная пирамида.</p><p>$a$ - сторона основания.</p><p>$h$ - высота пирамиды.</p><p><strong>Найти:</strong></p><p>Формулу объема $V$ для:</p><p>а) правильной треугольной пирамиды.</p><p>б) правильной шестиугольной пирамиды.</p><p><strong>Решение:</strong></p><p>Общая формула для вычисления объема любой пирамиды:</p><p>$V = \frac{1}{3}S_{осн}h$</p><p>где $S_{осн}$ — это площадь основания пирамиды, а $h$ — ее высота.Задача сводится к нахождению площади основания ($S_{осн}$) для каждого случая и подстановке ее в общую формулу объема.</p><p><strong>а) правильная треугольная пирамида</strong></p><p>В основании правильной треугольной пирамиды лежит правильный (равносторонний) треугольник со стороной $a$.</p><p>Площадь равностороннего треугольника вычисляется по формуле:</p><p>$S_{осн} = \frac{a^2\sqrt{3}}{4}$</p><p>Подставим эту площадь в формулу объема пирамиды:</p><p>$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{a^2\sqrt{3}}{4} \cdot h = \frac{a^2h\sqrt{3}}{12}$</p><p><strong>Ответ:</strong> $V = \frac{a^2h\sqrt{3}}{12}$</p><p><strong>б) правильная шестиугольная пирамида</strong></p><p>В основании правильной шестиугольной пирамиды лежит правильный шестиугольник со стороной $a$.</p><p>Правильный шестиугольник можно разделить на 6 одинаковых равносторонних треугольников со стороной $a$.</p><p>Площадь одного такого треугольника мы уже знаем из пункта а): $S_{\triangle} = \frac{a^2\sqrt{3}}{4}$.</p><p>Следовательно, площадь основания (правильного шестиугольника) равна сумме площадей шести таких треугольников:</p><p>$S_{осн} = 6 \cdot S_{\triangle} = 6 \cdot \frac{a^2\sqrt{3}}{4} = \frac{3a^2\sqrt{3}}{2}$</p><p>Теперь подставим полученную площадь основания в формулу объема пирамиды:</p><p>$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{3a^2\sqrt{3}}{2} \cdot h = \frac{a^2h\sqrt{3}}{2}$</p><p><strong>Ответ:</strong> $V = \frac{a^2h\sqrt{3}}{2}$</p>" ] #original: array:6 [ "id" => 1566106 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1023} "task" => array:2 [ "refs" => "1146625" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Правильная пирамида.</p><p>$a$ - сторона основания.</p><p>$h$ - высота пирамиды.</p><p><strong>Найти:</strong></p><p>Формулу объема $V$ для:</p><p>а) правильной треугольной пирамиды.</p><p>б) правильной шестиугольной пирамиды.</p><p><strong>Решение:</strong></p><p>Общая формула для вычисления объема любой пирамиды:</p><p>$V = \frac{1}{3}S_{осн}h$</p><p>где $S_{осн}$ — это площадь основания пирамиды, а $h$ — ее высота.Задача сводится к нахождению площади основания ($S_{осн}$) для каждого случая и подстановке ее в общую формулу объема.</p><p><strong>а) правильная треугольная пирамида</strong></p><p>В основании правильной треугольной пирамиды лежит правильный (равносторонний) треугольник со стороной $a$.</p><p>Площадь равностороннего треугольника вычисляется по формуле:</p><p>$S_{осн} = \frac{a^2\sqrt{3}}{4}$</p><p>Подставим эту площадь в формулу объема пирамиды:</p><p>$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{a^2\sqrt{3}}{4} \cdot h = \frac{a^2h\sqrt{3}}{12}$</p><p><strong>Ответ:</strong> $V = \frac{a^2h\sqrt{3}}{12}$</p><p><strong>б) правильная шестиугольная пирамида</strong></p><p>В основании правильной шестиугольной пирамиды лежит правильный шестиугольник со стороной $a$.</p><p>Правильный шестиугольник можно разделить на 6 одинаковых равносторонних треугольников со стороной $a$.</p><p>Площадь одного такого треугольника мы уже знаем из пункта а): $S_{\triangle} = \frac{a^2\sqrt{3}}{4}$.</p><p>Следовательно, площадь основания (правильного шестиугольника) равна сумме площадей шести таких треугольников:</p><p>$S_{осн} = 6 \cdot S_{\triangle} = 6 \cdot \frac{a^2\sqrt{3}}{4} = \frac{3a^2\sqrt{3}}{2}$</p><p>Теперь подставим полученную площадь основания в формулу объема пирамиды:</p><p>$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{3a^2\sqrt{3}}{2} \cdot h = \frac{a^2h\sqrt{3}}{2}$</p><p><strong>Ответ:</strong> $V = \frac{a^2h\sqrt{3}}{2}$</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1146626" "type" => "task" ] "previous" => array:2 [ "refs" => "1146624" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Book {#1028} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\BookPage {#1010 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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Задания (с. 149)
Условие. Задания (с. 149)
скриншот условия
Выведите формулу объема правильной:
а) треугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.
$V = \frac{\sqrt{3}}{12} a^2 h$
б) шестиугольной пирамиды, стороны основания которой равны $a$, а высота равна $h$.
$V = \frac{\sqrt{3}}{2} a^2 h$
Решение 2 (rus). Задания (с. 149)
Дано:
Правильная пирамида.
$a$ - сторона основания.
$h$ - высота пирамиды.
Найти:
Формулу объема $V$ для:
а) правильной треугольной пирамиды.
б) правильной шестиугольной пирамиды.
Решение:
Общая формула для вычисления объема любой пирамиды:
$V = \frac{1}{3}S_{осн}h$
где $S_{осн}$ — это площадь основания пирамиды, а $h$ — ее высота.Задача сводится к нахождению площади основания ($S_{осн}$) для каждого случая и подстановке ее в общую формулу объема.
а) правильная треугольная пирамида
В основании правильной треугольной пирамиды лежит правильный (равносторонний) треугольник со стороной $a$.
Площадь равностороннего треугольника вычисляется по формуле:
$S_{осн} = \frac{a^2\sqrt{3}}{4}$
Подставим эту площадь в формулу объема пирамиды:
$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{a^2\sqrt{3}}{4} \cdot h = \frac{a^2h\sqrt{3}}{12}$
Ответ: $V = \frac{a^2h\sqrt{3}}{12}$
б) правильная шестиугольная пирамида
В основании правильной шестиугольной пирамиды лежит правильный шестиугольник со стороной $a$.
Правильный шестиугольник можно разделить на 6 одинаковых равносторонних треугольников со стороной $a$.
Площадь одного такого треугольника мы уже знаем из пункта а): $S_{\triangle} = \frac{a^2\sqrt{3}}{4}$.
Следовательно, площадь основания (правильного шестиугольника) равна сумме площадей шести таких треугольников:
$S_{осн} = 6 \cdot S_{\triangle} = 6 \cdot \frac{a^2\sqrt{3}}{4} = \frac{3a^2\sqrt{3}}{2}$
Теперь подставим полученную площадь основания в формулу объема пирамиды:
$V = \frac{1}{3} \cdot S_{осн} \cdot h = \frac{1}{3} \cdot \frac{3a^2\sqrt{3}}{2} \cdot h = \frac{a^2h\sqrt{3}}{2}$
Ответ: $V = \frac{a^2h\sqrt{3}}{2}$
Другие задания:
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