Maths-

General

Easy

Question

# A Sphere and cube have the same surface. Show that the ratio of the volume of the sphere to that of the cube is

Hint:

### Volume of a sphere

Volume of cube a^{3}

## The correct answer is: √6:√π

### Explanation:

- We have given a sphere and a cube with same surface area.
- We have to prove that there ratio of volume of the sphere to that cube is

Step 1 of 1:

Let the radius of sphere and side of cube be r, a respectively.

So,

Surface area of sphere will be and surface area of cube be 6a^{2}

It is given that both surface area are equal.

So,

Now the volume of sphere will be

And volume of cube will be

Now ratio of their volume will be

Now ratio of their volume will be

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