Question

the diameter of moon is 1/4th diameter of earth .What fraction of moon volume is of earth?

Answer 1

Assuming planets are spherical but in reality they are not
!

And Volume is directly proportional to R^3.:

That's why

Volume of Moon is 1/64 Volume of Earth:

Answer 2

The answer is given below :

It is assumed that moon and earth are spheres. So we need to find the volume of spheres.

Now, if 8d units be the diameter of the earth, then 2d units is the diameter of the moon.

So, radius of the earth is 4d units and that of the moon is d units.

Then, volume of the earth is

$= \frac{4}{3} \times \pi \times {(4d)}^{3} \: {unit}^{3} \\ \\ = \frac{4}{3} \times \pi \times {4}^{3} \times {d}^{3} \: {unit}^{3} \\ \\ = \frac{4}{3} \times \pi \times 64 \times {d}^{3} \: {unit}^{3}$

and the volume of the moon is

$= \frac{4}{3} \times \pi \times {d}^{3} \: {unit}^{3}$

Thus the fraction of the volumes of the moon and the earth is

$= \frac{1}{64}$

(Just divide the volumes.)

Thank you for your question.