A cylindrical vessel with a base of radius 15 m and height of 21 m is filled with water to a certain height. 10 spherical balls of radius 1.5 m are dropped into this vessel. By how much will the level of water rise in the vessel?

Given:

Radius of cylindrical vessel = 15 m

Radius of spherical ball = 1.5 m

10 spherical balls are dropped into the vessel

Formula Used:

1. Volume of Sphere = (4/3)πr³

2. Volume of Cylinder = πR²h

Where, r = radius of sphere, R and h are radius and height of cylinder

Calculation:

Volume of 10 spherical balls = (4/3)π(1.5)³

10 spherical balls are dropped into the vessel

So, increase in water level is because of the volume of 10 spherical balls

Let the increase in water level be 'h'

⇒ πR2h = 10 × (4/3)πr3

⇒ h × (15)² = 10 × (4/3) × (1.5)³

⇒ h = \(\frac{10\times4×1.5× 1.5× 1.5}{3× 15× 15}\)

⇒ h = 0.2 m = 20 cm

∴ When 10 spherical balls of radius 1.5 m are dropped into this vessel, the water level rises by 20 cm.