Question

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

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Answer 1

Answer:

The ratio of their surface areas is 1 : 16

Step-by-step explanation:

Both the moon and earth are in the shape of spheres.

Surface area of a sphere of radius 'r' =4πr²

Let d1  be the diameter of the moon and d2 be the diameter of the earth.

Let r1 be the radius of the moon and r2 be the radius of the earth.

Given : d1 = 1/4 d2

2r1 = 1/4 2r2

r1 = 1/4 r2

Now, ratio of their surface areas is:

A1 : A2

= 4πr1² : 4πr2²

= r1² : r2²

= 1² : 4²

= 1 : 16

the ratio of their surface areas is 1 : 16