Need to determine resistance of an object

[Kruum]

Homework Statement

A material of resistivity p is formed into a solid, truncated cone of height
h and radii r_1 and r_2 at either end. Calculate the resistance of the cone
between the two flat ends.

You can find my awful sketch as a thumbnail.

Homework Equations

R=pL/A ,where p is resistivity.

The Attempt at a Solution

I know I need to calculate dR=(p*dy)/(pi*r^2). But I don't know what is r as a function of y.

 

[Mapes]

Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r₁ to r₂.

Where does the 4 come from in the denominator?

 

[Kruum]

Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r₁ to r₂.

Where does the 4 come from in the denominator?

Thank you. I'll try your tip. And the 4 was just a typing mistake.

I uploaded the image. It can be found here: http://www.aijaa.com/v.php?i=3584252.jpg

 

[Kruum]

This is what I came up with:

r = r₂+y*(r₁-r₂)/h

If I integrate dR, it gives me (p*h)/(pi*r₁*r₂).

Does that look okay?

 

[Mapes]

Looks good.

 

[Kruum]

Thanks for the help, Mapes!