A sphere of radius $5\ cm$ is immersed in water filled in a cylinder, the level of water rises $\frac{5}{3}\ cm$. Find the radius of the cylinder.

 Given:

A sphere of radius $5\ cm$ is immersed in water filled in a cylinder, the level of water rises $\frac{5}{3}\ cm$.

To do:

We have to find the radius of the cylinder.

Solution:

Radius of sphere $(r_1) = 5\ cm$

This implies,

Volume of the sphere $=\frac{4}{3} \pi r_{1}^{3}$

$=\frac{4}{3} \pi(5)^{3}$

$=\frac{500}{3} \pi \mathrm{cm}^{3}$

Height of the water level $=\frac{5}{3}\ cm$

Let $r$ be the radius of the cylinder.

Therefore,

Volume of water $=$ Volume of the sphere

$\pi r^{2} h=\frac{500}{3} \pi$

$\pi r^{2} \times \frac{5}{3}=\frac{500}{3} \pi$

$r^{2}=\frac{500}{3} \times \frac{3}{5}$

$r^2=100$

$r^2=(10)^{2}$

$\Rightarrow r=10$

Hence, the radius of the cylinder is $10 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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