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. 

Answer 1

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`