SOLUTION: A right circular cylinder of radius r and height h has volume given by V=πr^2h and surface area given by A=2πr^2+2πrh. A manufacturer must design a cylindrical can that can hold

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Question 1167048: A right circular cylinder of radius r and height h has volume given by V=πr^2h and surface area given by A=2πr^2+2πrh. A manufacturer must design a cylindrical can that can hold 800π cubic cm of liquid. Express the amount of matrial needed to make the can as a function of its radius, r.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A right circular cylinder of radius r and height h has volume given by V=πr^2h and surface area given by A=2πr^2+2πrh.
A manufacturer must design a cylindrical can that can hold 800π cubic cm of liquid.
Express the amount of material needed to make the can as a function of its radius, r.
:
Volume
pi%2Ar%5E2%2Ah+=+800pi
divide both sides by pi
r%5E2%2Ah+=+800
h+=+800%2Fr%5E2
:
Area
A+=+%282pi%2Ar%5E2%29+%2B+%282pi%2Ar%2Ah%29
replace h with 800%2Fr%5E2
A+=+%282pi%2Ar%5E2%29+%2B+%282pi%2Ar%2A%28800%2Fr%5E2%29%29
Cancel r
A+=+%282pi%2Ar%5E2%29+%2B+%282%2Api%2A%28800%2Fr%29%29
simplify
A+=+2pi%2A%28r%5E2%2B%28800%2Fr%29%29 amt of material as a function of r