Question

The radius of the earth is two times the radius of the moon. What fraction of the volume of the earth is the volume of the moon?

Answer 1

Answer:

The fraction is:

$\dfrac{1}{8}$

Step-by-step explanation:

We are given that the radius of the earth is two times the radius of the moon.

Let the radius of moon be r.

Then the radius of earth by above statement= 2 r.

As we know that both moon and earth are in shape of sphere hence for finding there volume we will use the formula of finding the volume of sphere.

Volume of earth(V')=

$\dfrac{4}{3}\times \pi\times (2r)^3\\\\=\dfrac{4}{3}\times \pi\times 8\times r^3\\\\=8\times (\dfrac{4}{3}\pi r^3)$

also Volume of moon(V)=

$\dfrac{4}{3}\times \pi\times r^3\\ \\=\dfrac{4}{3}\pi r^3$

Hence fraction of the volume of the earth to the volume of the moon is given by:

$\dfrac{V'}{V}\\\\=\dfrac{\dfrac{4}{3}\pi r^3}{8(\dfrac{4}{3}\pi r^3)}\\\\=\dfrac{1}{8}$

Hence the fraction is:

$\dfrac{1}{8}$