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

$dm=\frac{1}{4}de$........(i)

$\Rightarrow$volume of earth

$=\frac{4}{3}\pi \times {\left(\frac{de}{2}\right)}^3$

$\Rightarrow$volume of moon

$=\frac{4}{3}\pi \times {\left(\frac{dm}{2}\right)}^3$

so fraction

$=\frac{\frac{4}{3}\pi {\left(\frac{dm}{2}\right)}^3}{\frac{4}{3}\pi {\left(\frac{de}{2}\right)}^3}$

$={\left(\frac{dm}{de}\right)}^3={\left(\frac{1}{4}\right)}^3=\frac{1}{64}$........from (i)