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

Question

mote1985 [20]

2 years ago

6

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

Mathematics

2 answers:

Viktor [21]2 years ago

3 0

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

grandymaker [24] · Answer 1 · 2023-09-01T18:25:07+03:00

grandymaker [24]2 years ago

3 0

Answer: 2h

Step-by-step explanation: