Finding the Resistance of a cone

[aximwolf]

Homework Statement

A solid truncated cone is made of a material of resistivity 5.10 Ohm*m. The cone has a height h = 1.16 m, and radii a = 0.34 m and b = 0.84 m. Assuming that the direction of current is parallel to the axis of the cylinder, what is the total resistance for this cone? (Use "Ohm" as your units.)

Hint: You have to do an integral. Regard the cone as made of a stack of pancake-shaped resistors (of varying radius) in series. The thickness of each pancake is dx and you integrate from x = 0 to x = h. You need to work out a formula for the dependence of pancake radius r on x.

Homework Equations

R= rho*L/A
Where rho=resistivity

The Attempt at a Solution

I know that to find the resistance I need some Length divided by area of each infinite number of resistant pancake shape discs through the cone. The bounds of the integral are going to be 0 to h but I am not sure what to integrate. I know that both radius and area are changing but I am not sure how to integrate that. I know that rho is a constant so it can be taken out of the integral and will be multiplied to the result of the integral.

Please help me find the formula that relates dx to radius so that I can integrate that and than multiply it by the resistivity to get the resistance of the cone.

 

[aximwolf]

never mind i found that (0,a) and (h,b). The radius than equals pi((b-a/h)x +a)^2. Now i can easily set up the integral.