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Shyam · #4 December 1st, 2008, 02:19 PM

Quote:

Originally Posted by rlder35

I have two math problems that have me STUMPED! Can anyone help??

A cylindrical can is to hold 4PIE cubic inches of frozen concentrate orange juice. The cost per square inch of constructing the metal top and bottom is twice the cost per square inch of constructing the cardboard side. What are the dimensions of the least expensive can?

ANY help is greatly appreciated!!

Volume, $V = 4\pi \;\;in^3$

$\pi r^2 h = 4\pi$

$h=\frac{4\pi}{\pi r^2}$

$h = \frac{4}{r^2}$ .....................(1)

Now, surface area , $A= 2\pi r^2+2\pi rh$

Cost $C= 2\pi r^2\times 2+2\pi rh$

$C = 4\pi r^2 +2\pi r \left(\frac{4}{r^2}\right)$

$C = 4\pi r^2+\frac{8\pi}{r}\;\;\;$ Now, minimize this cost.