posted by Nancy on .
Express the amount of material needed to make a can as a function of the radius. In other words, find a function A(r) such that A represents the surface area (in square inches) of the cylinder and r is the radius (in inches).
my answer (not sure)
A(r) = r^2 + 2r + 29 ?
This looks like a continuation of your last problem
Visualize taking a tin can apart.
you would have 2 circles, the top and the bottom
plus the sleeve that forms the can.
Pretend you are opening it up by cutting along the height of the can.
Would you not have a rectangle whose length is the circumference of the circle, and whose width is the height ?
So the total area would be
top + bottom + rectangle
= πr^2 + πr^2 + (2πr)h, where h is the height.
= 2πr^2 + (2πr)h
This is precisely what I used in the previous question.
You will need the height, or else be able to calculate it like in your previous question when the volume was given.