Question

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1.) The diameter of moon is approximately one-fourth of the diameter of the earth. What fraction of volume of the earth is volume of moon ???

Answer 1

Let,

   the diameter of Earth be d.

According to Question,

       The diameter of moon be 1/4 d.

     ⇒   (d/D) = (1/4)

            (r/R) = (1/4)

Volume of moon / Volume of earth = 4/3$\pi$r^2/ 4/3$\pi$R^2

= $r^{3}$/$R^{3}$

= $^\frac{1}{4}^{3}$

=  1 /64

Hence, volume of moon is 1/64th of that of earth.

Answer 2

1)Let diameter of earth be D
Diameter of moon = D/4
Radius of Earth = D/2
Radius of moon = D/8
Earth and moon are like spheres
So Volume of Earth = 4/3pi(D/2)^3
and volume of moon = 4/3pi(D/8)^3
so ratio of their volumes= 512/8=64:1
Curved surface area of Earth = 4pi(D/2)^2
Curved surface area of moon = 4pi(D/8)^2
so ratio of their surface area = 64/4=16:1