Question

The diameter of the moon is approximately one-fourth the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

• A. $\frac{1}{4}$
• B. $\frac{1}{16}$
• C. $\frac{1}{64}$
• D. $\frac{1}{256}$

Answer 1

The correct option is C $\frac{1}{64}$

Let $d_1$ and $d_2$ be the diameters of the moon and the earth respectively.

Then, $d_1=\frac{1}{4}{d}_2$
$\Rightarrow$ $\frac{r_1}{r_2}=\frac{1}{4}$
We know that volume of sphere = $\frac{4}{3}\pi r^3$
$⟹\frac{\text{Volume of moon}}{\text{Volume of earth}}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}={\left(\frac{r_1}{r_2}\right)}^3={\left(\frac{{\frac{1}{4}r}_2}{r_2}\right)}^3={\left(\frac{1}{4}\right)}^3=\frac{1}{64}$