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

Volume of a cone $=\frac{1}{3}\pi \left(r^2\right)\left(h\right)$

By given data,

Volume of 3 cones $=$ volume of 1 big cone

$\Rightarrow \left[\frac{1}{3}\pi \right(r^2\left)\right(108\left)\right]\times 3=\frac{1}{3}\pi \left(20\right)\left(20\right)\left(9\right)$

$\Rightarrow r^2=\frac{20\times 20\times 9}{3\times 108}=11.111$

$\Rightarrow$ $r=3.333cm$