Is it possible to produce a continuous and oriented aramid fiber-epoxy matrix co

Question

Is it possible to produce a continuous and oriented aramid fiber-epoxy matrix composite having longitudinal and transverse moduli of elasticity of 57.1 GPa and 4.12 GPa, respectively? What should the volume fraction of the fiber be if the answer is yes? Assume that the modulus of elasticity of the epoxy is 2.4 GPa and the value of the modulus for aramid fibers is 131 GPa
Answer
A.
Yes, 32.5% fiber
B.
Yes, 42.5% fiber
C.
Yes, 47.5% fiber
D.
Yes, 50% fiber
E.
Yes, 12.5% fiber
F.
Do not have enough information to determine.
G.
No, it is not possible

Explanation / Answer

Fiber 42.5%

For longitudinal composite modulus
F(ef) = E(f)V(f) + E(m)V(m)
57.1 = 131V(f) + 2.4V(m)...eq 1

For Transverse composite modulus
1/F(et) = V(f)/E(f) + V(m)/E(m)

1/4.12 = V(f)/131 + V(m)/2.4 ...eq 2

Solving we get V(fiber) = 42.5%

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