Final answer:
The factor by which the radii of arterioles constrict to reduce blood flow to 1.00% is 0.10, calculated by taking the fourth root of 0.01 in accordance with Poiseuille's Law.
Step-by-step explanation:
To determine the factor by which the radii of the arterioles constrict, we must understand the relationship between the radius of a blood vessel and the rate of blood flow. According to Poiseuille's Law, the flow rate (Q) is proportional to the fourth power of the radius (r) of the vessel. Thus, if the flow rate is reduced to 1.00% of its original value, it means that the radius has been reduced to the fourth root of 0.01 (since 0.01 = 1% = 1/100).
The fourth root of 0.01 is 0.1, which means the radius must constrict by a factor of 0.1 to reduce the blood flow to 1%. Therefore, the correct answer is (b) 0.10.