Arectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm resistivity is ρ = 3.5×10−5 ω⋅m . determine the resistance for current that passes through the solid in -"g. com"

Missing part in the text of the question. Found the rest on internet:
"determine the resistance for current that passes through the solid in (a) the x direction (b) the y direction and (c) the z direction"

Solution

The relationship between resistance and resitivity is given by

where R is the resistance
is the resistivity of the material (for carbon, as in this problem, )
L is the length of the conductor
A is its cross-sectional area.

We can solve the 3 parts of the problem by using the same formula, but every time L and A will be different (because they will depend on the direction of the current)

(a)  the current is in the x-direction, so the length of the conductor is 

while the cross sectional area is

So the resistance in this case is


(b) the current is in the y-direction, so the length of the conductor is 

while the cross sectional area is

So the resistance in this case is


(c) the current is in the z-direction, so the length of the conductor is 

while the cross sectional area is

So the resistance in this case is