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Консультация № 198277
17.04.2020, 09:11
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Правильное ли моё решение? Заранее спасибо за ответ.
Правильное ли моё решение? Заранее спасибо за ответ.
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Обсуждение
17.04.2020, 09:13
общий
У правильной шестиугольной пирамиды отрезали вершину плоскостью, параллельной плоскости основания И проходящей через середину высоты пирамиды. Найдите объём получившегося многогранника, если объём отрезанной части равен 8.
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22.04.2020, 08:33
общий
это ответ
Здравствуйте, pelageya.romanyuk2002!
Решение правильное. Поскольку пирамиды SA[sub]1[/sub]B[sub]1[/sub]C[sub]1[/sub]D[sub]1[/sub]E[sub]1[/sub]F[sub]1[/sub] и SABCDEF подобны, и их высота отличается в 2 раза, то, исходя из принципа подобия, остальные линейные параметры также отличаются в 2 раза, площади граней (в том числе основания) - в 2[sup]2[/sup] = 4 раза, а объём - в 2[sup]3[/sup] = 8 раз. Следовательно, объём пирамиды SA[sub]1[/sub]B[sub]1[/sub]C[sub]1[/sub]D[sub]1[/sub]E[sub]1[/sub]F[sub]1[/sub] составляет 1/8 от объёма пирамиды SABCDEF, а объём многогранника - 7/8, то есть в семь раз больше.
Решение правильное. Поскольку пирамиды SA[sub]1[/sub]B[sub]1[/sub]C[sub]1[/sub]D[sub]1[/sub]E[sub]1[/sub]F[sub]1[/sub] и SABCDEF подобны, и их высота отличается в 2 раза, то, исходя из принципа подобия, остальные линейные параметры также отличаются в 2 раза, площади граней (в том числе основания) - в 2[sup]2[/sup] = 4 раза, а объём - в 2[sup]3[/sup] = 8 раз. Следовательно, объём пирамиды SA[sub]1[/sub]B[sub]1[/sub]C[sub]1[/sub]D[sub]1[/sub]E[sub]1[/sub]F[sub]1[/sub] составляет 1/8 от объёма пирамиды SABCDEF, а объём многогранника - 7/8, то есть в семь раз больше.
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