A 41.1-kg woman balances on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.698 cm, what pressure does she exert on the floor?
2. The attempt at a solution
Pressure is a force applied over an area. The woman has a weight (force) which is related to her mass and gravity. Since we're not told different, we'll assume she's standing on the surface of the Earth, where the acceleration of gravity is 9.8 m/s^2. So, her weight is
W = 41.1 kg * 9.8 m/s^2 = 402.78
Since she's balancing on the heel of one shoe, all her weight is applied over that area. The area is related to the radius by the familiar formula from geometry class,
A = pi * r^2
A = 3.14 * (0.698 cm)^2
A = 1.53 cm^2
So, the pressure is
P = W / A
P = 402.78 N / 1.53 cm^2
P = 263.25 N/cm^2
But it says incorrect. Did I mess up somewhere? Please help.