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Консультация № 177671
04.04.2010, 18:46
0.00 руб.
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1
1
здравствуйте,уважаемые эксперты.помогите пожалуйста решить задачу:
определить объём и поверхность тела,образуемого вращением равнобедренного треугольника вокруг боковой стороны,если основание равно 30 см,а боковая сторона 25 см.
заранее благодарен.
определить объём и поверхность тела,образуемого вращением равнобедренного треугольника вокруг боковой стороны,если основание равно 30 см,а боковая сторона 25 см.
заранее благодарен.
Обсуждение
Неизвестный
04.04.2010, 19:11
общий
это ответ
Здравствуйте, G-buck.
1) При вращении получим два конуса с общим основанием. Образующая одного конуса 25 см, а другого 30 см.
2)Высота, проведенная к основанию равнобедренного треугольника равна
√(25^2 - 15^2) = 20
Найдем высоту равнобедренного треугольника, проведенную к боковой стороне (это будет радиус основания конусов):
0,5*30*20 = 0,5 * h * 25
h= 24
3)Площадь поверхности тела:
S=pi*r*(l1+l2)
S= pi*20*55 = 1100pi
4)Объем тела:
V=1/3 *pi * r^2 * (h1+h2)
V = 1/3 *pi * 400 *25 = 10000/3 *pi
1) При вращении получим два конуса с общим основанием. Образующая одного конуса 25 см, а другого 30 см.
2)Высота, проведенная к основанию равнобедренного треугольника равна
√(25^2 - 15^2) = 20
Найдем высоту равнобедренного треугольника, проведенную к боковой стороне (это будет радиус основания конусов):
0,5*30*20 = 0,5 * h * 25
h= 24
3)Площадь поверхности тела:
S=pi*r*(l1+l2)
S= pi*20*55 = 1100pi
4)Объем тела:
V=1/3 *pi * r^2 * (h1+h2)
V = 1/3 *pi * 400 *25 = 10000/3 *pi
5
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