What are the different way for solving the question for class 9th question of Surface Areas and Volumes chapter of math of question no.7 of math please suggest me the best way for solving this question of exercise 13.4 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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The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. Q.7
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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