# Thread: Right Circular Cone Volume

1. ## Right Circular Cone Volume

The volume V of a right circular cone is V = (1/3)(pi)(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.

NOTE: What is a more simple way to say:

"...express the volume V as a function of r."

2. Originally Posted by symmetry
The volume V of a right circular cone is V = (1/3)(pi)(r^2)(h). If the height is TWICE the radius, express the volume V as a function of r.

NOTE: What is a more simple way to say:

"...express the volume V as a function of r."
Hello,

you've got 2 functions which should be composed:

$V = \frac{1}{3} \pi \cdot r^2 \cdot (h)$. Plug in the term for h:

$V = \frac{1}{3} \pi \cdot r^2 \cdot (2r)= \frac{2}{3} \pi \cdot r^3$

EB

3. ## ok

Understood but tell me, what is a more simple way to say:

"...express the volume V as a function of r"?

4. Originally Posted by symmetry
Understood but tell me, what is a more simple way to say:

"...express the volume V as a function of r"?
Hello,

that's a little bit tricky to answer for me.

In Germany we would say (literally translated of course!): "V of r"

But most of the time I'm leafing through my dictionary looking for the adequate expression. So don't trust me here.

EB

5. ## ok

Tell me, are you a math professor?

6. ## V as a function of r

"express V as a function of r" pretty much means make an equation with only V on one side of the equals sign, and r as the only variable on the other.

i.e. V = (2 / 3) * pi * r^3 (functions are usually written "f(r) = (2/3)*pi*r^3")

but NOT
V = (1 / 3) * pi * r^2 * h