Question

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

Answer 1

let the diameter of the earth be 'd'. then the diameter of the moon will be 'd/4'
radius of the earth = d/2
radius of the moon= 1/2 x d/4 = d/8
surface area of the moon = 4 x pi x (d/8)^2
surface area of the earth = 4 x pi x (d/2)^2
 required ratio= 4 pi(d/8)^2 ÷ 4 pi(d/2)^2
                      =4/64
                      = 1/16
 ∴the ratio between their surface areas is 1:16

Answer 2

⇒ Let the diameter of the earth be d metre.

⇒ And, the diameter of moon is d/4 metre.

⇒ V1 = Volume of earth

⇒ V2 = Volume of moon

⇒ Volume of sphere = 4/3 π (r^3)

⇒ V1 = 4/3π(d/2)^3

⇒ V1 = π/6(d)^3

⇒ V2 = 4/3π(d/8)^3

⇒ V2 = π/384(d)^3

⇒ V1/V2

⇒ 1/64