Question

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball of radius 9cm is dropped into the tube and thus level of water is raised by hcm. What is the value of h.

Answer 1

Given that radius of cylindrical tube (r₁) = 12cm

Let height of cylindrical tube (h)

Volume of a cylinder = `pir_1^2h`

v₁ = π(12)² x h                 ............(1)

Given spherical ball radius (r₂) = 9cm

Volume of sphere = `4/3pir_2^3`

`v_2=4/3xxpixx9^2`      ..............(2)

Equating (1) and (2)

v₁ = v₂

`pi(12)^2xxh=4/3xxpixx9^3`

`h=(4/3xxpixx9^3)/(pi(12)^2)`

h = 6.75cm

Level of water raised in tube (h) = 6.75cm