Question

The height of a cylinder varies inversely with its radius. If the height is doubled, what is the effect on the volume of the cylinder?

Answer 1

The height is the inverse of the radius:
\[r = \frac{1}{h}\]
\[V = \pi r^{2}h = \pi \left(\frac{1}{h} \right)^{2}h = \pi \frac{1}{h}\]
So if you double the height:\[V = \pi \frac{1}{2h}\]
The volume is halved. I'm pretty sure there's a more elegant way of doing this with calculus but this works too.

Answer 2

r=k/h

volume of cylinder= pi r^2 h
pi (k/2h)^2 (2h)

= pi (k/4h ) 2h = 1/4 *2 pi(k/h)^2 h = 1/2 r^2 h

Answer 3

I dont understand. Why are you guys saying r = k/h, but its h = k/r, "height varies inversely with radius". Does it matter which you put it as?