#### Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

#### Solution

Let the diameter of earth be *d*. Therefore, the diameter of moon will be d/4.

Radius of earth = d/2

`"Radius of moon "= 1/2xxd/4 = d/8`

`"Surface area of moon "= 4pi(d/8)^2`

`"Surface area of earth "= 4pi(d/2)^2`

`"Required ratio "=(4pi(d/8)^2)/(4pi(d/2)^2)=4/64=1/16`

Therefore, the ratio between their surface areas will be 1:16.

Is there an error in this question or solution?

Solution The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area. Concept: Surface Area of a Sphere.