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## Homework Statement

A dish, described by the equation x

^{2}+z

^{2}=e

^{y}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/m

^{3}and gravitational acceleration to be 9.8 m/s

^{2}.

## Homework Equations

I know that the work formula is

W= int(0 to h): F(y)dy+(T-h)(F(h)), and F(y

_{0})=(dens)(g.acc)(Volume above y

_{0}), 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 x

^{2}+z

^{2}=e

^{y}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(x

^{2}+z

^{2}) and x=sqrt(e

^{y}+z

^{2}) so far..