The largest sphere is to be carved out of a right circular cylinder of radius $ 7 \mathrm{~cm} $ and height $ 14 \mathrm{~cm} $. Find the volume of the sphere.

Given:

The largest sphere is to be carved out of a right circular cylinder of radius \( 7 \mathrm{~cm} \) and height \( 14 \mathrm{~cm} \).

To do:

We have to find the volume of the sphere.

Solution:

Radius of the right circular cylinder $=7\ cm$

Height of the right circular cylinder $=14\ cm$

Let $r$ be the radius of the largest sphere.

Largest sphere to be carved will have its diameter as the height of the cylinder.

Therefore,

$h=14 \mathrm{~cm}$

$\Rightarrow 2 r=14$

$r=\frac{14}{2}$

$r=7 \mathrm{~cm}$

This implies,

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

$=\frac{4}{3} \times \frac{22}{7} \times 7^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times 343$

$=\frac{4312}{3}$

$=1437.33 \mathrm{~cm}^{3}$

The volume of the sphere is $1437.33\ cm^3$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

31 Views

Kickstart Your Career

Get certified by completing the course

Get Started