Question

Using clay, a student made a right circular cone of height $48$ cm and base radius $12$ cm. Another student reshapes it in the form of a sphere. Find the radius of the sphere.

Answer 1

Consider the dimensions of cone

Given, height $h=48$ cm, radius $r=12$ cm

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

$=\frac{1}{3}\pi {\left(12\right)}^2\left(48\right)$cubic cm

$=\pi {\left(12\right)}^2\left(16\right)$cubic cm
Let $r$ be the radius of sphere.

Volume of sphere and cone will be equal.

Volume of sphere $=\pi {\left(12\right)}^2\left(16\right)$

$\Rightarrow \frac{4}{3}\pi r^3=\pi {\left(12\right)}^2\left(16\right)$

$\Rightarrow \frac{4}{3}\times \pi \times r^3=\pi \times 12\times 12\times 16$

$\Rightarrow r^3=3\times 3\times 12\times 16$

$\Rightarrow r^3=3\times 3\times 3\times 2\times 2\times 2\times 2\times 2\times 2$

$\Rightarrow r=3\times 2\times 2=12$ cm

Thus, radius of sphere $=12$ cm.