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Develop a formula for the SA of a cone

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Develop a formula for radius as a function of surface area for a cone with height three times its diameter.

    2. Relevant equations

    ∏rs + ∏r^2 = SA
    s = √(h^2+r^2)
    H = 3d or 6r

    3. The attempt at a solution

    Dont know what values to use for s = √(h^2+r^2).
     
    Last edited: Sep 16, 2012
  2. jcsd
  3. Sep 16, 2012 #2

    LCKurtz

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    You are given that the height is 3 times the diameter, so you can get s in terms of r. Put that in your formula for SA and solve for r in terms of SA.
     
  4. Sep 16, 2012 #3
    Would my h value be 3 and my r value be 0.5 ?
     
  5. Sep 16, 2012 #4
    I also realized I made the error 3D=1H instead of vice versa.
     
  6. Sep 16, 2012 #5

    LCKurtz

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    No, ##r## isn't given. It is one of the variables you are to use. It and SA are the variables in your requested equation. ##H = 3D = 6r##.
     
  7. Sep 16, 2012 #6
  8. Sep 16, 2012 #7

    LCKurtz

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    Why bother with that? You need s in terms of r to plug into your SA equation.
     
  9. Sep 16, 2012 #8
    s=√(h^2+6r^2), the answer is r=√SA/∏(1+√37). How do they get rid of the H ?
     
  10. Sep 16, 2012 #9
    Would that be the proper thing for S?
     
  11. Sep 16, 2012 #10

    LCKurtz

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    You have ##s=\sqrt{h^2+r^2}## and you have ##h = 6r##. Put that in for the ##h## in the ##s## equation. Then put that result in for the ##s## in your SA equation. Then solve that for ##r##.
     
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