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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 ?

  • algebra - ,

    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.

  • algebra - ,

    Thank you!!

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