# Homework Help: Develop a formula for the SA of a cone

1. Sep 16, 2012

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. Sep 16, 2012

### LCKurtz

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. Sep 16, 2012

Would my h value be 3 and my r value be 0.5 ?

4. Sep 16, 2012

I also realized I made the error 3D=1H instead of vice versa.

5. Sep 16, 2012

### LCKurtz

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. Sep 16, 2012

blah

7. Sep 16, 2012

### LCKurtz

Why bother with that? You need s in terms of r to plug into your SA equation.

8. Sep 16, 2012

s=√(h^2+6r^2), the answer is r=√SA/∏(1+√37). How do they get rid of the H ?

9. Sep 16, 2012

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 $r$.