Question

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

Answer 1

volume is directly proportional to cubic of diameter

volume of earth/volume of moon
= (diameter)³e/(diameter)³m
= (4d/d)³
=64
.

now surface area is directly proportional to square of diameter

surface area of earth/surface area of moon
=[4d/d]²
=16

hope this will help you........

Answer 2

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Let the diameter of earth be “d”. Therefore, the radius of earth will be will be $\frac{d}{2}$

Diameter of moon will be $\frac{d}{4}$ and the radius of moon will be $\frac{d}{8}$

Volume of the moon = $(\frac{4}{3}) πr³$

$= (\frac{4}{3}) π (\frac{d}{8})^3 = \frac{4}{3}π(\frac{d^3}{512})$

Volume of the earth = (4/3) πr³= (4/3) π (d/2)³= 4/3π(d³/8)

Fraction of the volume of the earth is the volume of the moon

=$\frac{volume \: of \: earth}{volume \: of \: moon} = \frac{\frac{4}{3}\pi \frac{{d}^{3} }{512} }{\frac{4}{3}\pi \frac{{d}^{3} }{8} } = \frac{8}{512} = \frac{1}{64}$

Volume of moon is of the $\frac{1}{64}$ volume of earth.