The Earth and Moon

The diameter of the Moon is approximately 1/4 of the diameter of the Earth. What fraction of the volume of the Earth is the volume of the Moon?

Correct answer:

r₂ =  1:64

Step-by-step explanation:

$$\begin{gathered} f_1=1/4=\frac{1}{4}=0.25 \\ {f}_1=r_1:r_2=d_1:d_2 \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r_1^3 \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r_2^3 \\ {f}_2=V_1:V_2 \\ {f}_2=\frac{\frac{4}{3}\cdot \pi \cdot r_1^3}{\frac{4}{3}\cdot \pi \cdot r_2^3} \\ {f}_2=\frac{r_1^3}{r_2^3} \\ {f}_2=(r_1/r_2{)}^3 \\ {r}_2=f_2=f_1^3=0.25^3\approx 0.0156=1:64 \end{gathered}$$

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