Question

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

Answer 1

Let the diameter of moon be d and earth be D
Given d = (1/4) D
Hence (d/D) = (1/4)
Hence (r/R) = (1/4)
Volume of moon / Volume of earth = (4/3)πr3 / (4/3)πR3
= r3 / R3
= (r/R)3
= (1/4)3
= 1/64
Hence volume of moon will be (1/64)th volume of earth.
Let the diameter of the earth be R and that of the moon will be R/4
The radius of moon and earth are R/8 and R/2 respectively
Ratio of their surface area
4π(R/8)²/4π(R/2)²
= 1/6
/1/4
=1/64×4/1
=1/16 = 1:16
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