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 ------------ (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

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

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.

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