F. if a 2 x 6 (which means the actual dimensions of the board are 1.5 in. x 5.5 in.) milled from the same wood (and therefore has the same density) weighs 3.2 lb, how long is the board?

By definition, we have to

W = V * Dw

W: weight

V: Volume

D: Density

Clearing and Substituting we have:

V = W / Dw = (3.2 lb) / (0.021 (lb / in ^ 3)) = 152.38 in ^ 3

Then, on the other hand, the volume is

V = l * w * d

l: long

w: width

d: depth

Clearing and substituting

l = V / (w * d) = (152.38 in ^ 3) / ((1.5 in) * (5.5 in)) = 18.5 in

The answer is 18.5 in