Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/3 of the height.
I tried (1/9) *pi * r^2 but it's wrong.

Question

Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/3 of the height.
I tried (1/9) *pi * r^2 but it's wrong.

wolf1728 · Answer

Cone Volume = (π • r² • h) / 3 
((3 • Cone volume) / π) =r² • h 
If you want to calculate the volume of a cone when h/3 = r then let h = 6 and r = 2 Volume = 25.133 

I think you want to calculate the relation between volume of a cone and radius but it seems the volume is connected both to the radius and the height.

blockcolder · Answer

It's supposed to be r^3, not r^2.

wolf1728 · Answer

blockcolder Visit this link http://math.about.com/od/formulas/ss/surfaceareavol_2.htm or here http://www.math.com/school/subject3/lessons/S3U4L4DP.html or here http://wiki.answers.com/Q/What_is_the_formula_for_volume_of_a_cone and you will see those sites state that the volume of a cone is: (π • r² • h) / 3

blockcolder · Answer

Yeah, and it was stated that the radius is 1/3 of height; i.e. r=h/3 or equivalently, h=3r. Thus, the formula for volume becomes $\frac{\pi r^2(3r)}{3}=\pi r^3$.
I should have clarified that I was referring to OP's formula, not yours. My bad.

wolf1728 · Answer

Okay blockcolder. Yeah and I think I was a little too "quick on the draw" in my reply.
And why hasn't mango213 shown up yet?

blockcolder · Answer

He's probably offline right now.

wolf1728 · Answer

Anyway, I'm glad we got our disagreement all cleared up.