Question

A child reshapes a cone made up of China clay of height $24cm$ and radius of base $6cm$ into a sphere. The radius of the sphere is:

• A. $24cm$
• B. $12cm$
• C. $6cm$
• D. $48cm$

Answer 1

The correct option is C $6cm$

Height of cone$,h=24$ cm

Radius of base$,r=6$ cm

Volume of cone$,v=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi \times 6\times 6\times 24=288\pi {cm}^3$

Now let the radius of the sphere be $R$ cm

Volume of the sphere made$=$ Volume of cone

$\Rightarrow \frac{4}{3}\pi R^3=288\pi \Rightarrow R^3=\frac{288\pi \times 3}{4\pi }=72\times 3=216R=\sqrt[3]{3216}=6$

Radius of sphere$=6$ cm