Question

diameter of the moon is approximatly one fourth of the diameter 9f the earth find the ratio of their srface area (1:16) ​

Answer 1

Step-by-step explanation:

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 ------------ (1)

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