Step 1: The pressure is given by the formula:
\[
P = \frac{F}{A}
\]
where \( F = \text{force} = \text{weight of the girl} = mg \), and \( A \) is the area of contact of the heel with the floor.
Step 2: The area of the circular heel is calculated using the formula:
\[
A = \pi r^2
\]
Given the diameter of the heel is \( 2 \, \text{cm} \), the radius \( r = 1 \, \text{cm} = 0.01 \, \text{m} \). Therefore:
\[
A = \pi (0.01)^2 = 3.14 \times 10^{-4} \, \text{m}^2
\]
Step 3: The force exerted by the girl is:
\[
F = mg = 31.4 \times 10 = 314 \, \text{N}
\]
Step 4: Now, the pressure is:
\[
P = \frac{314}{3.14 \times 10^{-4}} = 10^6 \, \text{Pa}
\]
Thus, the correct answer is \( 10^6 \, \text{Pa} \).