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Консультация № 197691
04.02.2020, 22:52
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В прямоугольном параллелепипеде ABCDA1B1C1D1 AD=6см, CD=8см, точка О - точка пересечения диагоналей грани АВСD. Угол наклона отрезка В1О к плоскости АВВ1 равен 30 градусов. Вычислите объём параллелепипеда АВСDA1B1C1D1.
В прямоугольном параллелепипеде ABCDA1B1C1D1 AD=6см, CD=8см, точка О - точка пересечения диагоналей грани АВСD. Угол наклона отрезка В1О к плоскости АВВ1 равен 30 градусов. Вычислите объём параллелепипеда АВСDA1B1C1D1.
Обсуждение
09.02.2020, 19:28
общий
это ответ
Здравствуйте, svrvsvrv!
Пусть точка K - середина ребра AB. Рассмотрим треугольник OKB1. Сторона OK параллельна AD и вдвое короче её, то есть OK = AD/2 = 6/2 =3 см. При этом OK перпендикулярна АВВ1, следовательно, плоскости треугольников OKB1 и АВВ1 также перпендикулярны между собой, и угол при вершине В1 треугольника OKB1 есть угол между отрезком В1O и плоскостью АВВ1, равный 30[$186$]. Тогда из прямоугольного треугольника OKB1
Теперь рассмотрим прямоугольный треугольник KBB1. Гипотенуза KB1 = 3[$8730$]3 см, катет KB = AB/2 = CD/2 = 8/2 = 4 см, тогда второй катет BB1 будет равен
Поскольку BB1 - боковое ребро параллелепипеда, то [$8730$]11 - его высота. Зная длину и ширину (8 и 6 см), можно найти объём: 8[$183$]6[$183$][$8730$]11 = 48[$8730$]11 см3.
Пусть точка K - середина ребра AB. Рассмотрим треугольник OKB1. Сторона OK параллельна AD и вдвое короче её, то есть OK = AD/2 = 6/2 =3 см. При этом OK перпендикулярна АВВ1, следовательно, плоскости треугольников OKB1 и АВВ1 также перпендикулярны между собой, и угол при вершине В1 треугольника OKB1 есть угол между отрезком В1O и плоскостью АВВ1, равный 30[$186$]. Тогда из прямоугольного треугольника OKB1
Теперь рассмотрим прямоугольный треугольник KBB1. Гипотенуза KB1 = 3[$8730$]3 см, катет KB = AB/2 = CD/2 = 8/2 = 4 см, тогда второй катет BB1 будет равен
Поскольку BB1 - боковое ребро параллелепипеда, то [$8730$]11 - его высота. Зная длину и ширину (8 и 6 см), можно найти объём: 8[$183$]6[$183$][$8730$]11 = 48[$8730$]11 см3.
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