- #1

- 72

- 0

## Homework Statement

A conical container with radius 1, height 2 and with its base centred on the ground

at the origin contains food. The density of the food at any given point is given by

D(r) = a/(z + 1) where a is a constant and z is the height above the base.

Using cylindrical polar coordinates, calculate the total mass of food in the container.

## Homework Equations

## The Attempt at a Solution

ok so mass is the integral D(r)dV, and in cylindrical coordinates dV is rdrd[tex]\theta[/tex]dz

I thought that you could probably do:

[tex]\int^1_0 \,dr[/tex][tex]\int^{2\pi}_0 \,d\theta[/tex][tex]\int^{2r-2}_0 \,dz[/tex]

[tex](ra/(z+1))[/tex]

But this makes the integral very difficult and I don't think it's right. I'm pretty sure there's something wrong with my limits on dz. Any help would be appreciated