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Консультация № 197070
13.11.2019, 18:37
0.00 руб.
23.11.2019, 13:10
0
1
1
Здравствуйте,
Вычислить объём тела, ограниченного поверхностями
Вычислить объём тела, ограниченного поверхностями
Обсуждение
23.11.2019, 13:56
общий
это ответ
Здравствуйте, mustang289!
Тело представляет собой часть области внутри параболоида x[sup]2[/sup] + y[sup]2[/sup] = 16 - [$960$]z/2, ограниченную снизу плоскостью z = 0. Для удобства расчётов перейдём к цилиндрическим координатам по формулам x = r cos [$966$], y = r sin [$966$], z = z, dV = r d[$966$] dr dz. Тогда для данного тела имеем 0 [$8804$] [$966$] [$8804$] 2[$960$], 0 [$8804$] r [$8804$] 4, 0 [$8804$] z [$8804$] 2/[$960$](16 - r[sup]2[/sup]), и его объём будет равен
Тело представляет собой часть области внутри параболоида x[sup]2[/sup] + y[sup]2[/sup] = 16 - [$960$]z/2, ограниченную снизу плоскостью z = 0. Для удобства расчётов перейдём к цилиндрическим координатам по формулам x = r cos [$966$], y = r sin [$966$], z = z, dV = r d[$966$] dr dz. Тогда для данного тела имеем 0 [$8804$] [$966$] [$8804$] 2[$960$], 0 [$8804$] r [$8804$] 4, 0 [$8804$] z [$8804$] 2/[$960$](16 - r[sup]2[/sup]), и его объём будет равен
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