Question

The diameter of the moon is approximately 1/4th of the Earth. What will be the ratio of their volumes?
$v = \frac{4}{3}\pi {r}^{2}$
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Answer 1

Let A and B be two spheres with radii $r_A[tex] and [tex]r_B$, respectively. The ratio between their volumes is

$\dfrac{\frac{4}{3}\pi r_A^3}{\frac{4}{3}\pi r_B^3}=\dfrac{r_A^3}{r_B^3}=\left(\dfrac{r_A}{r_B}\right)^3$

So, the ratio of the volumes of two spheres is the cube of the ratio between the radii.

Since the two radii are in ratio 1:4, the two volumes will be in ratio 1:64, since 4^3=64.

So, the volume of the Earth is about 64 times the volume of the Moon.