1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

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


    User Avatar
    Science Advisor

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook