## anonymous 4 years ago 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?

1. anonymous

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.

2. anonymous

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

3. anonymous

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?