Work/Parametric Equations

Homework Statement

A dish, described by the equation x2+z2=ey for 0 < y < 10cm (or equal too) is filled 5cm high with milk. How much work does it take to spill all the milk on the floor? Take milk density to be 1030 Kg/m3 and gravitational acceleration to be 9.8 m/s2.

Homework Equations

I know that the work formula is
W= int(0 to h): F(y)dy+(T-h)(F(h)), and F(y0)=(dens)(g.acc)(Volume above y0), but I am stuck at the volume part of the equation.
It should be V(y)=int(0 to y): A(y), where the area is Pi(r)2. This is where I get stuck. How do I convert the x2+z2=ey into a radius function? So far, nobody's been able to explain parametrics to me very clearly even with just x and y, but now there's a z variable and I'm just clueless.

The Attempt at a Solution

I got y=ln(x2+z2) and x=sqrt(ey+z2) so far..

Dick
Homework Helper
Isn't x^2+z^2=e^y a circle in the x-z plane with radius e^y?

so then is it just the integral of pi(ey)2?

In which case V(y)= Pi((1/2)(e2y)) from 0-5, and a constant Pi((1/2)(e2(5))) from 5-10cm?

Dick