Develop a formula for the SA of a cone

[zaddyzad]

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).

 

[LCKurtz]

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.

 

[zaddyzad]

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 ?

 

[zaddyzad]

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

 

[LCKurtz]

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. $H = 3D = 6r$.

 

[zaddyzad]

blah

 

[LCKurtz]

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.

 

[zaddyzad]

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

 

[zaddyzad]

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?

 

[LCKurtz]

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 $r$.