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Консультация № 130849
06.04.2008, 18:53
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помогите решить задачу.
Найти объм правильной четырехугольной пирамиды, боковое ребро которой равно 12 сантиметров и образует угол с высотой 30 градусов.
заранее спасибо.
Найти объм правильной четырехугольной пирамиды, боковое ребро которой равно 12 сантиметров и образует угол с высотой 30 градусов.
заранее спасибо.
Обсуждение
Неизвестный
06.04.2008, 19:12
общий
это ответ
Здравствуйте, Александр КУ!
Высота этой пирамиды падает в центр основания, то есть в центр квадрата.
Рассмотрим прямоугольный треугольник, гипотенуза которого - боковое ребро, один из катетов - высота пирамиды, а второй - половина диагонали квадрата.
Высота лежит против угла 30 градусов, следовательно равна половине гипотенузы, то есть 6 см.
Половина диагонали квадрата: 6√3
Тогда вся диагональ: 12√3
Сторона квадрата: 12√3/√2
Площадь основания: (12√3/√2)^2 = 216
V = 1/3 * 216* 6 = 432
Высота этой пирамиды падает в центр основания, то есть в центр квадрата.
Рассмотрим прямоугольный треугольник, гипотенуза которого - боковое ребро, один из катетов - высота пирамиды, а второй - половина диагонали квадрата.
Высота лежит против угла 30 градусов, следовательно равна половине гипотенузы, то есть 6 см.
Половина диагонали квадрата: 6√3
Тогда вся диагональ: 12√3
Сторона квадрата: 12√3/√2
Площадь основания: (12√3/√2)^2 = 216
V = 1/3 * 216* 6 = 432
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