Answer
The radius is reduced by a factor of 1.3.
Work Step by Step
Use Poiseuille’s equation. The volume flow rate Q is proportional to the fourth power of the radius if other factors are held constant. In other words, $\frac{Q}{R^4}$ is constant. We are told that the initial Q is reduced by 65 percent.
$$\frac{Q_{final}}{R^4_{final}}=\frac{Q_{initial}}{R^4_{initial}}$$
$$R_{final}=(\frac{Q_{final}}{Q_{initial}})^{1/4}R_{initial}$$
$$R_{final}=(0.35)^{1/4}R_{initial}=0.769 R_{initial}$$
The radius is decreased by a factor of 1/0.769 = 1.3.
