Why aren't these two solutions the same (for a pipe system)

you need to use a weighted average, but you're not executing it correctly.

the general formula for a weighted average is

Sum(weights) * weighted_average = Sum[ weight * measure ]
or using symbols

Sum[ i=1,N; w_i ] * weighted_average_of_x = Sum[ i=1,N; w_i x_i ]

so your length weighted average is not correct. (the sum of the weights is (1+2+3+4), so you need to divide by 10, not 4.

likewise, your volume weighted average should be

Sum[ volume_i ] * volume_weighted average_of_diameter = Sum[ volume_i * diameter_i ]

This should make sense because you've seen it before: like when you compute center of mass (it's the mass weighed average of distance from a point) or the average velocity of an object (it's the mass weighted average of the velocities of all the objects in a system.)

It is not clear the purpose of this exercise is so it is impossible to give an answer.

im not sure