Answer:
volume fraction of fibers is 0.4
Step-by-step explanation:
Given that for the aligned carbon fiber-epoxy matrix composite:
Diameter (D) = 0.029 mm
Length (L) = 2.3 mm
Tensile strength (
) = 610 MPa
fracture strength (
) = 5300 MPa
matrix stress (
) = 17.3 MPa
fiber-matrix bond strength (
) = 19 MPa
The critical length is given as:

Since the critical length is greater than the length, the aligned carbon fiber-epoxy matrix composite can be produced.
The longitudinal strength is given by:

making Vf the subject of the formula:

Vf is the volume fraction of fibers.
Therefore:

volume fraction of fibers is 0.4