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Консультация № 197700
04.02.2020, 23:35
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
В треугольной пирамиде SABC сечение, параллельное боковой грани АSB, делит ребро АС в отношении 2:3, считая от точки С. Вычислите расстояние от точки С до плоскости АSB, если площадь сечения равна 20см2, а объём пирамиды равен 100см3.
В треугольной пирамиде SABC сечение, параллельное боковой грани АSB, делит ребро АС в отношении 2:3, считая от точки С. Вычислите расстояние от точки С до плоскости АSB, если площадь сечения равна 20см2, а объём пирамиды равен 100см3.
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Обсуждение
09.02.2020, 21:07
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это ответ
Здравствуйте, svrvsvrv!
Площадь любого сечения, параллельного грани АSB, будет пропорциональна квадрату расстояния от него до точки C. В данном случае грань ASB расположена в 5/2 раз дальше данного сечения от точки S, поэтому её площадь будет в (5/2)2 = 25/4 раз больше площади сечения и составит 25/4[$183$]20 = 125 см2. Объём любой пирамиды равна одной трети произведения площади её основания на высоту (расстояние от основания до вершины). В данном случае, если взять грань ASB за основание, а вершиной считать точку C, то для расстояния d между ними будет выполняться равенство 100 = 1/3[$183$]125[$183$]d, откуда d = 3[$183$]100/125 = 2.4 см.
Площадь любого сечения, параллельного грани АSB, будет пропорциональна квадрату расстояния от него до точки C. В данном случае грань ASB расположена в 5/2 раз дальше данного сечения от точки S, поэтому её площадь будет в (5/2)2 = 25/4 раз больше площади сечения и составит 25/4[$183$]20 = 125 см2. Объём любой пирамиды равна одной трети произведения площади её основания на высоту (расстояние от основания до вершины). В данном случае, если взять грань ASB за основание, а вершиной считать точку C, то для расстояния d между ними будет выполняться равенство 100 = 1/3[$183$]125[$183$]d, откуда d = 3[$183$]100/125 = 2.4 см.
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