Question

A cone of height 24cm and radius of base 6cm is made up modelling clay. A child moulds it in the form of sphere. Find the radius of the sphere.

Answer 1

Given that, the child reshapes cone with a sphere.

So, the volume of sphere$=$Volume of cone.

Height of cone$h=24$cm and radius of cone $=r=6$cm

$\Rightarrow \frac{4}{3}\pi r^3=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{4}{3}{r}^3=\frac{1}{3}\times 6^2\times 24$

$\Rightarrow r^3=\frac{1}{4}\times 864{cm}^3$

$\Rightarrow r={(3\times 72)}^{\frac{1}{3}}$

$\Rightarrow r={(2^3\times 3^3)}^{\frac{1}{3}}$

$\therefore r=6$cm

Hence,radius of the sphere$=6$cm