Question

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

(a) 2 : 1

(b) 1 : 1

(c) 2 : 3

(d) 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) =

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) =

Now, the ratio of the volume of sphere to the volume of the cylinder =

So, the ratio of the volume of sphere to the volume of the cylinder is . Therefore, the correct option is (c)