Resistivity

I did R = pL/A, where p is the resistivity, L = 20 and A = 4 x 20 x d

But the answer is to do p x 20 x d/4 x d^2

Could anyone explain why they have done that please?

Also:
Show that the number density of free electrons within the block is about 2 × 10^28 m^–3. Assume that each phosphorus atom contributes one free electron.

n = 1/d^3, but surely thats only finding the number density in one atom?

A is the cross sectional area... the area of a slice orthogonal to the direction of current flow.

I did R=ρL/A and got 224Ω which seems to be what the question is after

A=4 d² ~ 5.77E-19 m²
L=20d ~ 7.6E-9 m

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number density is the number of free electrons per m³ so it'd be the same for one atom as for a rectangular block of 80 atoms as shown in the picture.

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as usual the mark sheme isn't a model answer or an example of the exam board's favourite style.

I did R = pL/A, where p is the resistivity, L = 20 and A = 4 x 20 x d

But the answer is to do p x 20 x d/4 x d^2

Could anyone explain why they have done that please?

Also:
Show that the number density of free electrons within the block is about 2 × 10^28 m^–3. Assume that each phosphorus atom contributes one free electron.

n = 1/d^3, but surely thats only finding the number density in one atom?