Maintaining Volume in a Cylinder: Solving for the Necessary Radius Adjustment

[Paradiselovek]

please help me thank you so much ^^(I need help quick before the due date thanks)

Here the problem:

A soup company decides to increase the height of its can by 30% but to maintain their present volume. To the nearest percent, how much must the radius of the can be decreased to hold the volume constant.

(there a picture of the can which is a plain cyclinder)

I try working backward for the equation to find the volume of a cyclinder
, but i really don't know if I got that right. please help me

 

[phreak]

So the volume for a cylinder is pi r^2 h. Since we're increasing the height by 30%, this just means that we multiply h by 1.3 to get the new height. So let's call h the original height, and V the volume. Then we have:

V = pi r^2 h = pi (r0)^2 (1.3h), and we need to solve for r0, which is our new radius. Clearly, pi doesn't factor in so we have the equation r^2 h = 1.3 (r0)^2 h. I take it you can solve for r0.

 

[Paradiselovek]

So the volume for a cylinder is pi r^2 h. Since we're increasing the height by 30%, this just means that we multiply h by 1.3 to get the new height. So let's call h the original height, and V the volume. Then we have:

V = pi r^2 h = pi (r0)^2 (1.3h), and we need to solve for r0, which is our new radius. Clearly, pi doesn't factor in so we have the equation r^2 h = 1.3 (r0)^2 h. I take it you can solve for r0.

Oh thanks but I still don't get why is it r0?