Question

A right circular cone of height $8.4cm$ and the radius of its base is $2.1cm$. It is melted and recast into a sphere. Find the radius of the sphere.

Answer 1

We have.
$r=$ radius of the base of the cone$=2.1cm$
$h=$ height of the cone$=8.4cm$

Volume of the cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times {\left(2.1\right)}^2\times 8.4{cm}^3$

Let $R$ cm be the radius of the sphere obtained by recasting the melted cone.

Then volume of the sphere $=\frac{4}{3}\pi R^3$

Since the volume of the material in the form of cone and sphere remains the same
$\therefore \frac{4}{3}\pi R^3=\frac{1}{3}\times \pi \times {\left(2.1\right)}^2\times \left(8.4\right)$

$\Rightarrow R^3=\frac{{\left(2.1\right)}^2\times 8.4}{4}={\left(2.1\right)}^3\Rightarrow R=2.1cm$