Question

A cone is $8.4cm$ high and the radius of its base is $2.1cm$. It is melted and recast into a sphere. The radius of the sphere is

• A. $4.2cm$
• B. $2.1cm$
• C. $2.4cm$
• D. $1.6cm$

Answer 1

The correct option is B $2.1cm$

Volume of the cone $=\frac{1}{3}\pi r_c^{2}h$

Volume of the sphere $=\frac{4}{3}\pi r_s^3$

$r_c$ is the radius of cone $=2.1$ cm ....(Given)

Let $r_s$ be the radius of the sphere

$h$ is the height of cone $=8.4$ cm ...(Given)

Volume of cone $=$ Volume of sphere ...(Given)

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

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

$\Rightarrow r_s^3=9.261$

$\Rightarrow r_s=2.1$ cm