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Math Help - Applications of Differentiation Question Please help...

  1. #1
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    Applications of Differentiation Question Please help...

    Here is the question...
    "A industrial tank is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the tank must be 3000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost."

    Can anyone do this and explain to me how its solved? Thanks in advance.
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  2. #2
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    \frac{4}{3}\pi r^3 + \pi r^2 h = 3000

    use the equation above to solve for h in terms of r, then sub into the cost equation below to get cost as a function strictly of r ...

    C = 2(4\pi r^2) + 2\pi r h

    ... then determine \frac{dC}{dr} and minimize.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    \frac{4}{3}\pi r^3 + \pi r^2 h = 3000

    use the equation above to solve for h in terms of r, then sub into the cost equation below to get cost as a function strictly of r ...

    C = 2(4\pi r^2) + 2\pi r h

    ... then determine \frac{dC}{dr} and minimize.
    Ohhh okay. I didn't realize you had to write the area equation in the cost equation like that. Thanks a ton.
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