Question

Please help me finish up this related rates problem! Will post it below.

Answer 1

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 ((4 pi r^3)/(3))+ (pi)(r^2)(y-r). y is height and r is radius.originally, the candy box was designed to have a height of 6 inches and a radius of 2 inches, but the box needs to be slightly shorter. you need to adjust the box so that the height is 5.75 inches but v remains constant. find the value of dr/dy at the point r=2 and y=6. use the value to approximate the new radius

Answer 2

So far, I have found dr/dy and know that for y=6 and r=2 dr/dy equals -1/5

Answer 3

I am just confused about how to use -1/5 to find the new radius. @campbell_st ? Any chance you could help?

Answer 4

Or @sithsandgiggles?

Answer 5

I just figured it out! the new r=(11.5)/6 right?