With the question An oceanographer is studying how the ion concentration in seaw

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With the question
An oceanographer is studying how the ion concentration in seawater depends on depth. She makes a measurement by lowering into the water a pair of concentric metallic cylinders at the end of a cable and taking data to determine the resistance between these electrodes as a function of depth. The water between the two cylinders forms a cylindrical shell of inner radius ra, outer radius rb, and length L much larger than rb. The scientist applies a potential difference ?V between the inner and outer surfaces, producing an outward radial current I. Let ? represent the resistivity of the water.
We realize that we integrate resistivity(Length/area) but then from the solution shown we integrate dR= resistivity(dr/(2pirL)) We understand everything but why the L goes to the bottom of this integration.
Thanks.

Explanation / Answer

in the formula R = L/A, L is the length along the current, A is the area perpendicular to the current. In this problem, current is from a to b, and A is the surface area of the cylinder with radius r and length L, so A = 2rL.

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