Sketch a cylinder with radius r and h. What will change the volume of the cylinder more, doubling the radius or doubling the height. Explain your reasoning.

2. Originally Posted by Johnathon324
Sketch a cylinder with radius r and h. What will change the volume of the cylinder more, doubling the radius or doubling the height. Explain your reasoning.
$V_{cylinder}={\pi}r^2h={\pi}rrh$

If you double the height, the new volume in terms of the original height is

${\pi}rr(2h)$

What do you get if you double the radius ?

3. Pie times radius to the 4th power times height?

4. Originally Posted by Johnathon324
Pie times radius to the 4th power times height?
No, you are guessing!
Mathematics is concise

${\pi}(2r)(2r)h={\pi}(2)(2)rrh={\pi}4rrh=4{\pi}r^2h$

How does that compare to the case where you doubled the height ?