Question

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

Answer 1

$\huge\bold{Answer}$

Radius of earth => x .
Radius of moon => $\frac{x}{4}$
$<b>$
As the radius of moon is 1 / 4of the earth .. so as we have taken radius of earth as = x so, we have to take radius of moon= x / 4

${\boxed {\boxed {\boxed{\underline{\sf{Formula\: used}}}}}}$
$<b>$
=> $\frac{4}{3}$ π ${r}^{3}$

$\frac{Earth\: radius }{Moon\: radius }$ = $\frac{4}{3}πx^3$/$\frac{4}{3}πx^3$

$\frac{Re}{Rm}$ =>$\frac{4}{3}πx^3$/ $\frac{4}{3}π$$\frac{x}{4}^3$

1=]]] Cut 4/ 3 by 4/ 3 ....
2=]]] Cut π x^3 from πx^2

$\huge\bold{Final\: Answer}$==>>$\frac{1}{64}$

Answer 2

Solution :

Radius of the Moon = 1/4 of the Earth.

Let the Radius be 'y'

Then ,

Radius of the Moon = y/4

Using Formula :-

➨ 4/3 πr³

Now ,

The fraction of the volume of the earth is the volume of the moon = Radius of the Earth /Radius of the moon.

➨ 4/3 πr³ /4/3 πy/4³

➨ 1/64  ( Cutting the fraction, radius and π )

➨ 1/64