Question

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

Answer 1

hiiiii


let diameter of earth = D

diameter of moon =D/4

=) radius of earth = D/2

=) radius of moon = D/8

earth and moon are like spheres.

so volume 0f earth = 4/3×π(D/2)^3

and volume of moon = 4/3 × π(D/8)^3

so ratio of their volumes

= 512/8 = 64:1

curved surface area of earth = 4π(D/2)^2

curved surface area of moon = 4π(D/8)^2

so ratio of their surface area


= 64/4 = 16:1 

________________-_-___________

Hope it will help u

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