Question

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.

Answer 1

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

$\therefore Volume=\frac{4}{3}\pi r_1^3=\frac{4}{3}\pi (5{)}^3=\frac{500}{3}\pi c{m}^3$
Level of water rises in the cylinder after immersing the sphere in it
$\therefore$ Height of water level $=\frac{5}{3}cm$
Let r be radius of the cylinder, then volume of water = Volume of the sphere
$\pi r^{2}h=\frac{500}{3}\pi \Rightarrow \pi r^2\times \frac{5}{3}=\frac{500}{3}\pi \Rightarrow r^2=\frac{500}{3}\times \frac{3}{5}=100=(10{)}^2\therefore r=10cm$
Hence, radius of cylinder = 10 cm