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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
= `1/3pi xx 20^2 xx 9`
Volume of smaller cone
= `1/3pi xx r^2 xx 108`
Volume of larger cone = 3 × Volume of smaller cone
`1/3pi xx 20^2 xx 9 = 1/3pi xx r^2 xx 108 xx 3`
`=> r^2 = (20^2 xx 9)/(108 xx 3)`
`=> r = 20/6 = 10/3`
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