Question

A cone has height $h$ and a base with radius $r$ . You want to change the cone so its volume is doubled. What is the new height if you change only the height

Answer 1

Answer: 2h

Explanation:

Answer 2

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=\stackrel{doubled}{2V} \end{cases}\implies 2V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\pi r^2 h}{3\cdot 2} \\\\\\ V=\cfrac{\pi r^2}{3}\cdot \cfrac{h}{2}\implies V=\cfrac{\pi r^2\left( (h)/(2) \right)}{3}\qquad \textit{half the previous`