Develop a formula for the SA of a cone

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Homework Statement



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

Homework Equations



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

The Attempt at a Solution



Dont know what values to use for s = √(h^2+r^2).
 
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Answers and Replies

  • #2
LCKurtz
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Homework Statement



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

Homework Equations



∏rs + ∏r^2 = SA
s = √(h^2+r^2)
3h=1d or 2r

The Attempt at a Solution



Dont know what values to use for s = √(h^2+r^2).

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.
 
  • #3
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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.

Would my h value be 3 and my r value be 0.5 ?
 
  • #4
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I also realized I made the error 3D=1H instead of vice versa.
 
  • #5
LCKurtz
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Would my h value be 3 and my r value be 0.5 ?

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##.
 
  • #6
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blah
 
  • #7
LCKurtz
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I derived r = √(s^2-h^2)/6. Can you check that ?

Why bother with that? You need s in terms of r to plug into your SA equation.
 
  • #8
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s=√(h^2+6r^2), the answer is r=√SA/∏(1+√37). How do they get rid of the H ?
 
  • #9
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Why bother with that? You need s in terms of r to plug into your SA equation.

Would that be the proper thing for S?
 
  • #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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