Question

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is 

Options

• 2 : 1

• 1 : 1

•  2 : 3

•  1 : 2

Answer 1

In the given problem, we need to find the ratio between the volume of a sphere and volume of a circumscribing right circular cylinder. This means that the diameter of the sphere and the cylinder are the same. Let us take the diameter as d.

Here,

Volume of a sphere (V₁) = `(4/3) pi (d/2)^3`

`(4/3) pi (d^3/8)`

`= (pi d^3 ) /6`

As the cylinder is circumscribing the height of the cylinder will also be equal to the height of the sphere. So,

Volume of a cylinder (V₂) = `pi (d/2)^2 h`

`= pi d^2/4(d)`

`=(pi d^3)/4`

Now, the ratio of the volume of sphere to the volume of the cylinder = `V_1/V_2`

`V_1/V_2=(((pid^3)/6))/(((pi d^3)/4))`

         `=4/6`

          `=2/3`

So, the ratio of the volume of sphere to the volume of the cylinder is  2: 3 .