Question

a cylindrical vessel of diameter 18CM contains water. if iron spherical balls of radius 3 cm are immersed in water, then the no. of balls required to raise the level of water by 4 cm in the cylinder is?

Answer 1

Hi ,

Dimensions of a cylinder :

diameter ( D ) = 18 cm

radius ( R ) = D/2 = 18/2 = 9 cm

level of water raised after iron balls

immersed in water = ( H ) = 4 cm

Dimensions of each iron ball :

radius ( r ) = 3 cm

Let the number balls immeresed = n

Now ,

n × volume of each ball = volume of water raised

n × ( 4/3 ) × π r³ = π R² H

n = ( π R² H )/ [ ( 4/3 ) π r³ ]

n = (3 R² H ) /4r³

= ( 3 × 9 × 9 × 4 )/ ( 4 × 3 × 3 × 3 )

= 9

Therefore ,

Number of iron balls immersed = n = 9

I hope this helps you.

: )