Question

Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ------\\ r=\frac{h}{5}\implies 5r=h \end{cases}\implies V=\cfrac{\pi r^25r}{3} \implies V=\cfrac{5\pi r^3}{3}$