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Question
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm
Solution
Let the radius of the smaller cone be 'r' cm.
Volume of larger cone
`1/3pixx20^2xx9`
Volume of smaller cone
=`1/3pixxr^2xx108`
Volume of larger cone = 3 × Volume of smaller cone
`1/3pixx20^2xx9=1/3pixxr^2xx108xx3`
`⇒ r^2=(20^2xx9)/(108xx3)`
`⇒r=20/6=10/3`
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