Question

if the hieght and radius of the cone is tripled then find the ratio of Volume of the new cone and of that of original

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=\stackrel{3\times r}{3r}\\ h=\stackrel{3\times h}{3h} \end{cases}\implies V=\cfrac{\pi (3r)^2(3h)}{3} \\\\\\ V=\cfrac{\pi (3^2r^2)(3h)}{3}\implies V=\cfrac{\pi (9r^2)(3h)}{3}\implies V=27\left( \cfrac{\pi r^2 h}{3} \right)$

notice the original, and the new one, with the tripled "r" and "h" is just, whatever the original was times 27, namely 27 times as large as the original.