Question

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 ?

Answer 1

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.

Answer 2

Thank you!!