Heat Transfer - Conduction

JSBeckton

A truncated cone 30cm high is made of Aluminum. The dia at the top is 7.5cm, and 12.5cm at the bottom. The lower surface is maintained at 93 deg C, the upper surface at 540 deg C. the other surface is insulated. Assuming 1 dimentional heat flow, calculate the rate of heat transfer in watts.

Ok, my book is seriously lacking in the example department, and we have only gone through derivations in class, no examples yet.

I understand that this is a conduction problem so I am to use fouriers law

q=-kA dT
dx

k= 202 W/mC for Al

Now the tricky part, I know that the problem that I face is that the area changes along the axis. Am I just to integrate:

pi r^2 from 3.25cm to 6.25cm, then multiply that by (540-93)/.3?

Thanks