#### 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.

#### Solution

Given that radius of cylindrical tube (r_{1}) = 12cm

Let height of cylindrical tube (h)

Volume of a cylinder = `pir_1^2h`

v_{1} = π(12)^{2} x h ............(1)

Given spherical ball radius (r_{2}) = 9cm

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

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

Equating (1) and (2)

v_{1} = v_{2}

`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

Is there an error in this question or solution?

Solution 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_____? Concept: Volume of a Combination of Solids.