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

1.	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.
Answer» Radius of sphere = 5 cm Let ‘r’ be the radius of cylinder. We know, Volume of sphere = \(\frac{4}{3}\)πr³ = \(\frac{4}{3}\) x π x (5)³ Height (h) of water rises is \(\frac{5}{3}\) cm Volume of water rises in cylinder = πr²h Therefore, Volume of water rises in cylinder = Volume of sphere So, πr²h = \(\frac{4}{3}\)πr³ πr² x \(\frac{5}{3}\) = \(\frac{4}{3}\) x π x (5)³ or r² = 100 or r = 10 Therefore, radius of the cylinder is 10 cm.

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.

Answer»

Radius of sphere = 5 cm

Let ‘r’ be the radius of cylinder.

We know, Volume of sphere = \(\frac{4}{3}\)πr³

= \(\frac{4}{3}\) x π x (5)³

Height (h) of water rises is \(\frac{5}{3}\) cm

Volume of water rises in cylinder = πr²h

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

So, πr²h = \(\frac{4}{3}\)πr³

πr² x \(\frac{5}{3}\) = \(\frac{4}{3}\) x π x (5)³

or r² = 100

or r = 10

Therefore, radius of the cylinder is 10 cm.