Question

Find the ratio of surface area of moon to earth if ratio of volume of earth is 64:1​

Answer 1

Answer:

$\frac{volume \: of \: earth}{volume \: of \: moon} = \frac{64}{1}$

$\frac{ \frac{4}{3}\pi {e}^{3} }{ \frac{4}{3}\pi {m}^{3} } = \frac{64}{1}$

where,e and m are radius of earth and moon respectively.

$\frac{e}{m} = \frac{4}{1}$

$\frac{surface \: area \: of \: moon}{surface \: area \: of \: earth} = \frac{ {6\pi \: m}^{2} }{ {6\pi \: e}^{2} }$

$\frac{surface \: area \: of \: moon}{surface \: area \: of \: earth} = \frac{1}{16}$

Therefore, Required ratio is 1:16...