Question

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 1

Volume of sphere = `4/3πr^3`

= `4/3π(5)^3`

∴ Volume of water rise in cylinder = Volume of sphere
Let r be the radius of the cylinder

`πr^2h=4/3πr^3`

⇒`r^2×5/3=4/3(5)^3`

⇒`r^2=20×5`

⇒`r^2=200`

⇒`r^1=10cm`

Answer 2

In the given problem, a sphere is immersed in a water filled cylinder and this leads to a rise in the water level by 5/3 cm. Here, we need to find the radius of the cylinder.

Given here,

Radius of the sphere (r_s) = 5 cm

Rise in the level of water in cylinder (h) = 5/3 cm

So, let us take the radius of the cylinder (r_c) = x cm

Now, according to the problem, the volume of the sphere will be equal to the increase in the volume of the cylinder.

Volume of the sphere = increase in volume of the water in cylinder

`(4/3) π r_c^2  = pi  r_c^2 h`

`(4/3 )pi (5)^3 = pi (x)^2 (5/3)`

                `x^2 = ((4/3)(5)^3)/((5/3))`

               `x^2 =((4)(5)^3(3))/((3)(5))`

               `x^2 = 100`

Further,

`x^2 = 100`

`x = sqrt(100) `

x=10 cm 

Therefore, the radius of the cylinder is 10 cm .