Question

A solid sphere of radius $r$ is melted and cast into the shape of a solid cone of height $r$. Find the radius of the base of the cone.

Answer 1

Let the radius of cone $=R$

Height of cone $=r$

as per the question, since sphere is cast into a cone

$⟹$ Volume of cone $=$ volume of sphere

$⟹\frac{1}{3}\pi \times R^2\times r=\frac{4}{3}\pi r^3$

$⟹R^2=4r^2=(2r{)}^2$

$⟹R=2r$

$\therefore$ The radius of cone is $2r$