# Right Circular Cone Volume

• Jan 21st 2007, 05:05 AM
symmetry
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."
• Jan 21st 2007, 05:29 AM
earboth
Quote:

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:

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

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

EB
• Jan 22nd 2007, 01:24 PM
symmetry
ok
Understood but tell me, what is a more simple way to say:

"...express the volume V as a function of r"?
• Jan 24th 2007, 10:55 AM
earboth
Quote:

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
• Jan 24th 2007, 01:01 PM
symmetry
ok
Tell me, are you a math professor?
• Jan 24th 2007, 01:04 PM
dcline
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