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Homework Help: Volume of a cone is 10 cubic cm

  1. Oct 4, 2005 #1
    volume of a cone is 10 cubic cm....

    Q: a cone shaped paper drinking cup holds 10 cubic cm of water. We would like to find the height and radius that will require the least amount of paper.

    Volume of a cone is: (b x h)/3, or with radius is: ((pi r squared x h))/3.

    I think you solve this problem by finding a ratio and getting h in terms of r. Any ideas? Thank you!
     
  2. jcsd
  3. Oct 4, 2005 #2
    You know:

    [tex]\text{V}=\frac{\pi\,r^{2}\,h}{3}=10[/tex]

    If I remember correctly, the surface area (what you want to minimize) is:

    [tex]\text{S}=\pi\,r\,\sqrt{r^{2}+h^{2}}[/tex]

    Now minimize this taking into consideration the restraint on volume.
     
    Last edited: Oct 4, 2005
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