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): $2.1cm$

Given, the height of the cone $=8.4cm$

Radius of the base $=2.1cm$

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

$=\pi \times 4.41\times 2.28c{m}^3$

The cone is melted and recast into a sphere.

Let the radius of a sphere be R.

Then, volume of the sphere = volume of the cone

$\Rightarrow \frac{4}{3}\pi R^3=\pi \times 4.41\times 2.8$

$\Rightarrow R^3=\frac{4.41\times 2.8\times 3}{4}$

$\Rightarrow R^3=4.41\times 0.7\times 3$

$\Rightarrow R^3=4.41\times 2.1$

$\therefore R=2.1$

Hence, the radius of the sphere is $2.1cm.$