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Homework Help: Optimization- oh how the brain hurts!

  1. Nov 6, 2005 #1
    Q: A solid if formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cm^3. Find the radius of the cylinder that produces the minimum surface area.

    OK, I got about halfway through my problem before I got lost.
    V of shpere= 4/3(pi)r^3
    V of cylinder= (pi)r^2(h)
    total V= 2(4/3*pi*r^30) + (pi*r^2*h)

    12=pi*r^2(2*4/3*r+h) which turns into 12/pi*r^2=8/3*r+h
    so h=(12/pi*r^2) - (8/3*r)

    Now I'm lost.
  2. jcsd
  3. Nov 7, 2005 #2


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    And what is the surface area as a function of r and h?
  4. Nov 7, 2005 #3


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    The problem was to minimize the surface area. You have done nothing with the surface area. What is the surface area of a sphere of radius r? What is the area of the curved surface of a cylinder or radius r and length h?
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