Introduction:
The solubility product constant (Ksp) is a measure of the extent to which a sparingly soluble salt dissolves in water. It represents the equilibrium constant for the dissociation of the salt into its constituent ions in solution. In this case, we are given the solubility product constant of Fe3+ hydroxide (Fe(OH)3) as 1.8×10^-37. We need to determine the pH of a saturated solution of Fe3+ hydroxide in distilled water.

Solubility Equilibrium of Fe(OH)3:
Fe(OH)3 (s) ⇌ Fe3+ (aq) + 3OH- (aq)

Expression for Solubility Product Constant:
The solubility product constant expression for Fe(OH)3 can be written as follows:
Ksp = [Fe3+][OH-]^3

Assumptions:
Before proceeding, we need to make some assumptions:
1. The dissociation of Fe(OH)3 is the only significant source of Fe3+ and OH- ions in solution.
2. The concentration of OH- ions is much greater than the concentration of H+ ions due to the dissociation of water.

pOH of the Saturated Solution:
Since Fe(OH)3 is a sparingly soluble salt, the concentration of Fe3+ ions can be assumed to be negligible. Thus, we can consider that:
[OH-] = 3[Fe3+]

Substituting this into the expression for Ksp, we get:
Ksp = [Fe3+][3[Fe3+]]^3
1.8×10^-37 = 27[Fe3+]^4

Taking the fourth root on both sides and solving for [Fe3+], we get:
[Fe3+] ≈ 1.29×10^-10

pOH to pH Conversion:
Since we are asked to find the pH of the solution, we need to convert the pOH of the saturated solution to pH. The relationship between pH, pOH, and the concentration of H+ and OH- ions is given by the equation:
pH + pOH = 14

Calculating pH:
To find the pOH of the solution, we can use the equation:
pOH = -log10[OH-]

Substituting the value of [OH-] ≈ 3[Fe3+], we get:
pOH ≈ -log10(3[Fe3+])

Using the concentration of [Fe3+] ≈ 1.29×10^-10, we can calculate the pOH:
pOH ≈ -log10(3×1.29×10^-10) ≈ 9.89

Finally, we can calculate the pH by subtracting the pOH from 14:
pH ≈ 14 - 9.89 ≈ 4.11

Conclusion:
The pH of a saturated solution of Fe3+ hydroxide in distilled water is approximately 4.11. Therefore, the correct option is a) 4.