Question

# When a right triangle of area 3 is rotated 360o about its shorter leg, the solid that results has a volume of 30. Calculate the volume of the solid if the same right triangle is rotated about its longer leg.

A
0.99
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B
7.9
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C
8.88
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D
31.42
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E
41.12
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Solution

## The correct option is B 7.9Let the length of shorter leg be h, length of longer leg be k , volume of resulting solid is 30.The resulting solid is cone, so volume is 13×πk2h=30Area of triangle is 12×hk=3 , which implies hk=6which gives 13×π6k=30 , k=15πVolume when rotated with longer leg is 13×πh2k=2πh=2π6k=12π15×π=7.9

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