The maximum number of #10 THHN copper conductors that can be installed in a 3/4 inch rigid metal conduit?

C

Area filled by one wire:

a = pi*d^2/4

Area available in the interior of a conduit:

A = pi*D^2/4

According to the NEC, the maximum you are permitted to fill a conduit is 40% of its total area. Thus, we construct the equation of:

0.4*A = n*a

Solve for n:

n = 0.4*A/a

Substitute:

n = 0.4*(pi*D^2/4)/(pi*d^2/4)

n = 0.4*D^2/d^2

Data:

Diameter of #10THWN: d = 0.149 in

Interior diameter of 3/4" RMC: D = 0.836 in

Note: usually the trade size of a conduit is approximately the interior diameter. It is generally a conservative estimate to assume that interior diameter is exactly the trade size. The value I listed is from the second and third linked sources.

The first source provides the diameter of #10THWN / #10THHN

Result:

n = 12.59

We must round down to make our answer make sense:

n = 12

choice D