Question

Please help with a related rates problem! Will fan and medal!

Answer 1

okay

Answer 2

A candy company needs a custom box for their truffles. The box they've chosen is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= 1/2(4r^2pi/3) + r^2pi(y-r), where y is the height of the box and r is the radius. Originally the candy box was designed to have a height of 6 inches and a radius of 2, but the shipper suggests that the boxes be made slightly shorter. You now need to adjust the radius so that the height is reduced to 5.75 but the volume remains constant. A. Find the value of dr/dy at the point r =2, r = 6.
I did some work already, will post that too

Answer 3

okay

Answer 4

r = 2, y = 6, right?

Answer 5

I solved that V=64pi/3 and that I am looking for a rearranged V to be r(y) to find dr/dy... but however I rearranged 64pi/3=1/2(4r^2pi/3) + r^2pi(y-r) I could not get r on its own

Answer 6

You do realize that finding dr/dy is only the first part. The second part is, you have to replace y = 5.75 to find r while keeping the volume constant

Answer 7

?

Answer 8

Yes, but I am trying to solve for dr/dy first because you have to

Answer 9

3/11 = dr/dy

Answer 10

I am trying to actually solve this, I don't want an answer