Question

The diameter of Moon is Approximately one-fourth of the diameter of the Earth. What fraction of the volume of Earth is to the volume of the Moon .

Answer 1

$\boxed{\boxed{\boxed{\purple{Hello \:Dear\:Students}}}}$

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✴Let the diameter of the Earth be 2x.

✴ The radius of the earth = $\frac{d}{2}$ = $\frac{2x}{2}$ = x

$\boxed{Daimeter\:of\:Moon:}$

=》$\frac{1}{4}$ × Daimeter of Earth

=》$\frac{1}{4}$ × 2x

=》$\frac{x}{2}$

✴ Radius of the Moon = $\frac{d}{2}$

= $\frac{\frac{x}{2}}{2}$

= $\frac{x}{4}$

$\textbf{Volume\:of\:Earth=}$ $\frac{4}{3}\pi{r}^{3}$

=》 $\frac{4}{3}\pi{x}^{3}$

$\textbf{Volume\:of\:Moon=}$ $\frac{4}{3}\pi{r}^{3}$

=》 $\frac{4}{3}\pi{\frac{x}{4}}^{3}$

=》 $\frac{4}{3}\pi\frac{{x}^{3}}{64}$

$\frac{Volume\:of\:Moon}{Volume\:of\:Earth }$=$\frac{ \frac{4}{3}\pi \frac{ {x}^{3} }{64} }{ \frac{4}{3}\pi {x}^{3} }$

=》 $\frac{Volume\:of\:Moon}{Volume\:of\:Earth }$ =$\frac{1}{64}$

Volume of Moon=$\frac{1}{64}$×Volume of Earth

So hence; The Volume of Moon is $\frac{1}{64}$ of Volume of Earth .

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Hope this helps. . . . . . ☺☺

Answer 2

⇒ Let the diameter of the earth be d metre.

⇒ And, the diameter of moon is d/4 metre.

⇒ V1 = Volume of earth

⇒ V2 = Volume of moon

⇒ Volume of sphere = 4/3 π (r^3)

⇒ V1 = 4/3π(d/2)^3

⇒ V1 = π/6(d)^3

⇒ V2 = 4/3π(d/8)^3

⇒ V2 = π/384(d)^3

⇒ V1/V2

⇒ 1/64