Question

The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth

Answer 1

$\bf \begin{array}{llll} \textit{surface area of a sphere}\\\\ s=4\pi r^2 \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3} \end{array}\quad \begin{cases} r=radius\\ -----\\ r=3960 \end{cases} \\\\\\\\ \cfrac{s}{V}\qquad \cfrac{4\pi 3960^2}{\frac{4\pi 3960^3}{3}}\implies \cfrac{\frac{4\pi 3960^2}{1}}{\frac{4\pi 3960^3}{3}}\implies \cfrac{4\pi 3960^2}{1}\cdot \cfrac{3}{4\pi 3960^3} \\\\\\ \cfrac{3}{3960}\implies \cfrac{1}{1320}$