# A sphere of radius 5 cm is immersed in water filled in a cylinder,

Question:

A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises 5/3 cm. Find the radius of the cylinder.

Solution:

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

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

Height of water rised = 5/3cm

Volume of water rised in cylinder $=\pi r^{2} h$

Therefore, Volume of water rises in cylinder = Volume of sphere

Let r be the radius of the cylinder

$\pi r^{2} h=4 / 3 \pi r^{3}$

$r^{2} \times 5 / 3=4 / 3 \times \pi \times(5)^{3}$

$r^{2} \times 5 / 3=4 / 3 \times 22 / 7 \times 125$

$r^{2}=20 \times 5$

$r=\sqrt{100}$

r = 10 cm