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प्रश्न
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.
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उत्तर
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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