Finding the electron drift speed

[MBBphys]

Homework Statement

A piece of n-type germanium is 2.0mm wide and 0.25 mm thick. At a certain temperature, the number of conduction electrons per cubic metre is 6 x 10²⁰ m^-3. What is the average drift speed of the electrons when a current of 1.5 mA flows? (e=1.6 x 10^-19

Homework Equations

I=nAve

The Attempt at a Solution

So I converted all the units to SI base.

1.5/1000 = 6 x 10²⁰ x (0.125/1000)² x pi x 1.6 x 10^-19 x v

v = 318.309...

v=318 metres per second (3sf).

But the answer booklet gives 31 metres per second. Am I wrong or is it wrong?

Thanks!

 

[Khashishi]

You are wrong. I got 31m. Where did 0.125 and pi come from? I don't see any circles in the problem statement. It has a thickness and a width --- that sounds like a rectangular prism.

 

[MBBphys]

Ah, right, so I have to do [(2/1000)*(0.25/1000)] rather than use pi, because it is a cuboid and not a circular piece of wire? I think because I usually do questions based on copper wires that are circular, I assumed the same here, but clearly that is wrong!

Thank you