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Консультация № 194453
17.01.2019, 21:07
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти объем тела, ограниченного поверхностями: y2+z2=(x−2)2, x=3, x=6
Внимание! В ответе указать только коэффициент при π
Найти объем тела, ограниченного поверхностями: y2+z2=(x−2)2, x=3, x=6
Внимание! В ответе указать только коэффициент при π
Обсуждение
21.01.2019, 10:32
общий
это ответ
Здравствуйте, valeriy.tvv!
Перепишем заданное уравнение поверхности второго порядка так:
Видно, что задан конус второго порядка с вершиной в точке
Положим 
Тогда заданное тело ограничено конусом второго порядка
вершина которого в системе координат
находится в начале координат, и плоскостями
Его можно рассматривать как тело, полученное вращением трапеции с вершинами в точках
вокруг оси 
Объём этого тела
(ед. объёма).
Ответ:
Перепишем заданное уравнение поверхности второго порядка так:
Видно, что задан конус второго порядка с вершиной в точке
Положим Тогда заданное тело ограничено конусом второго порядкавершина которого в системе координат
находится в начале координат, и плоскостямиЕго можно рассматривать как тело, полученное вращением трапеции с вершинами в точках
вокруг оси Объём этого тела (ед. объёма).Ответ:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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