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Question

If the height and radius of a cone of volume V are doubled, then the volume of the cone will be _____.

A

3V
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B

4V
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C

6V
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D

8V
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Solution

The correct option is D
8V

Let r and h be the radius and height of a cone, then

V=13πr2h

Let V be the volume of the new cone formed when the radius and height are doubled.

V=13π(2r)2(2h)=13π×4r2×2h=8(13πr2h)=8V


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