Question

The diameter of the moon is approximately one -fourth of the diameter of earth. compare of their volumes and curved surface areas

Answer 1

let diameter of Moon =Dm
diameter of earth = 4Dm

volume of Moon/volume of earth = 4πRm³/4πRe³ = Dm³/De³ =Dm³/8Dm³
= 1/8 = 1:8

surface area of Moon /surface area of earth = 4πRm²/4πRe² = Dm²/De²
=Dm²/4Dm² = 1/4 = 1:4

Answer 2

Solution:-

Let the diameter of earth be 'x'
Then the radius of the earth will be x/2 

Diameter of moon is 1/4 of the earth's diameter.
So, moon's diameter will be x/4
And radius of the moon will be x/8

Volume of the moon = 4/3πr³
⇒ 4/3*π*(x/8)³
⇒ 1/512*4/3*π*x³

Volume of the earth = 4/3πr³
⇒ 4/3*π(x/2)³
⇒ 1/8*4/3*π*x³

Now,

Volume of the moon/Volume of the earth

(1/512*4/3*π*x³)/(1/8*4/3*π*x³)
⇒ 8/512
= 1/64 
= 1 : 64
So, the volume of the moon is 1/64th of the volume of the earth.

Curved surface area of the moon = 4/3πr²
⇒ 4/3*π*(x/8)²
⇒ 1/64*4/3*π*x²

Curved surface area of the earth = 4/3πr²
⇒ 4/3*π*(x/2)²
⇒ 1/4*4/3*π*x²

CSA of moon/CSA of earth

⇒ (1/64*4/3*π*x²)/(1/4*4/3*π*x²)
⇒ 4/64
⇒ 1/16
= 1 :16
So, the CSA of the moon is 1/16th of the CSA of the earth.

Answer