Question

A spherical ball, $6$ cm in diameter, is melted and cast into a conical mould, the base of which is $12$ cm in diameter. Find the height of the cone.

Answer 1

Given diameter of spherical ball $D=6cm$

radius of spherical ball $r_1=\frac{D}{2}=3cm$

diameter of cone base $d=12cm$

radius of cone base $r=\frac{d}{2}=6cm$

Let $h=$ height of cone

Since the spherical ball is melted and recast into cone
Volume of spherical ball $=$ Volume of cone

$\Rightarrow \frac{\pi r_1^3}{3}=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{6^3}{6}=\frac{1}{3}\times {12}^2\times h$

$\Rightarrow h=0.75$ cm