Question

the diameter of the moon is approximately 1/4 of the diameter of the earth. find the ratios of their surface area​

Answer 1

1:16

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

Step by step-

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 = 4πr2

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 - eq1

Now, the surface area of earth = 4πR2

The surface area of moon = 4πr2

The ratio of their surface areas = 4πr2/4πR2

= r2/R2

= (r/R)2

= (1/4)2 [From equation(1)]

= 1/16

The ratio of their surface areas = 1:16