Calculating Resistivity of a Cylinder with a Hole

[Alexstre]

Homework Statement

A cylinder of radius a with a hole through it (of radius a/2) is filled with a material of resistivity p_2. Show that the total resistivity is now 4*(pL / pi*a²) (p_2 / 3p_2 + p)

Homework Equations

R=pL/A

The Attempt at a Solution

I started with a full cylinder and a single value of p:
R=pL/pi*a²

Then worked my way to a cylinder with a hole in it (empty):
A_full - A_hole = pi*a² - pi*(a/2)² and found A= (3/4)*pi*a² so:
R = (4/3) * pL / pi*a²

Now I know that I need to add both values of p somehow, but I'm unsure of the relation between 2 materials with different values of p.

 

[vela]

Think of it as two resistors in parallel.