# Triple Integral in Cylindrical Coords

1. May 3, 2012

### DTskkaii

1. The problem statement, all variables and given/known data
Construct a triple integral in cylindrical coords to find the volume of the cone r=z, where the height (z value) is limited by z=L.
Should be in the form => {int[b,a] int[d,c] int[f,e]} (r) {dr dtheta dz}
(Sorry for weird formatting above, brackets purely to make terms more discernible)
Then evaluate using this order of integration to find volume.

2. Relevant equations
Volume of a cone => V=[(pi)(a)^2(L)]/3
In a cylindrical coord system, r=z describes an inverted cone of infinite height

3. The attempt at a solution
Currently working on an attempt, but if someone could help out with the understanding, that would be great. It doesn't immediately make alot of sense to me.
i.e. r=z gives infinite height, but the volume is limited by L, so how do I find limits for that? Also can't see any immediate limits for theta in this situation.

2. May 4, 2012

### clamtrox

What do you mean? The limits you are given are $0 \ge z \ge L$ and $0 \ge r \ge z$. Everything is bounded here. Try drawing a picture to see why the limits are as they are.

3. May 4, 2012

### sharks

I think you mean: $0 \le z \le L$ and $0 \le r \le z$

4. May 4, 2012

### clamtrox

Whoops! Indeed L>0 :)