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Консультация № 197699
04.02.2020, 23:31
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
На рисунке 32, б изображена прямая треугольная призма ABCA1B1C1, длины всех рёбер которой равны. Точка О - середина ребра АС. Вычислите объём пирамиды В1ОВС, если известно, что площадь боковой поверхности призмы равна 48см2.
На рисунке 32, б изображена прямая треугольная призма ABCA1B1C1, длины всех рёбер которой равны. Точка О - середина ребра АС. Вычислите объём пирамиды В1ОВС, если известно, что площадь боковой поверхности призмы равна 48см2.
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Обсуждение
09.02.2020, 20:47
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это ответ
Здравствуйте, svrvsvrv!
Поскольку все рёбра призмы равны, то три её боковые грани (составляющие боковую поверхность) - равные между собой квадраты площадью 48/3 = 16 см2 со стороной [$8730$]16 = 4 см. Следовательно, высота призмы (и пирамиды В1ОВС) равна 4 см, а в основании пирамиды лежит прямоугольный треугольник ОВС c с гипотенузой BC = 4 см, катетом OC = AC/2 = 4/2 = 2 см и вторым катетом
Площадь этого треугольника составит OC[$183$]OB/2 = 2[$183$]2[$8730$]3/2 = 2[$8730$]3 см2, а объём пирамиды В1ОВС будет равен 1/3[$183$]2[$8730$]3[$183$]4 = 8/[$8730$]3 см3.
Поскольку все рёбра призмы равны, то три её боковые грани (составляющие боковую поверхность) - равные между собой квадраты площадью 48/3 = 16 см2 со стороной [$8730$]16 = 4 см. Следовательно, высота призмы (и пирамиды В1ОВС) равна 4 см, а в основании пирамиды лежит прямоугольный треугольник ОВС c с гипотенузой BC = 4 см, катетом OC = AC/2 = 4/2 = 2 см и вторым катетом
Площадь этого треугольника составит OC[$183$]OB/2 = 2[$183$]2[$8730$]3/2 = 2[$8730$]3 см2, а объём пирамиды В1ОВС будет равен 1/3[$183$]2[$8730$]3[$183$]4 = 8/[$8730$]3 см3.
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