Question

A right circular metallic cone of height $20$cm and base radius $5$cm is melted and recast into a sphere. Find the radius of the sphere.

Answer 1

Volume of cone $=$ Volume of sphere

$\Rightarrow \frac{1}{3}\pi r_1^{2}h=\frac{4}{3}\pi r_2^3\Rightarrow 5\times 5\times 20=4\times r_2^3$

$\Rightarrow r_2=\sqrt[3]{35\times 5\times 5}=5cm$

$\therefore$ Radius of sphere is $5cm$.