# The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

**Solution:**

Given: The diameter of the moon is approximately one-fourth of the diameter of the earth.

Since the moon and earth are spherical in shape, so the surface area of a sphere of radius r, SA = 4πr^{2}

Let the radius of the earth be R and the radius of the moon be r.

Diameter of the moon = 1/4 × diameter of the earth

Thus, the radius of the moon = 1/4 × radius of the earth [Since, radius = 2 × Diameter]

r = 1/4 × R

r/R = 1/4 ------------ (1)

Now, the surface area of earth = 4πR^{2}

The surface area of moon = 4πr^{2}

The ratio of their surface areas = 4πr^{2}/4πR^{2}

= r^{2}/R^{2}

= (r/R)^{2}

= (1/4)^{2} [From equation(1)]

= 1/16

The ratio of their surface areas = 1:16

**Video Solution:**

## The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.4 Question 7:

**Summary:**

It is given that the diameter of the moon is approximately one-fourth of the diameter of the earth. We have found that the ratio of their surface areas is 1:16.