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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?
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?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The 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.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0r=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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I 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?
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