Jean Poiseuille, a physician, developed a mercury filled U-tube to measure blood pressure in 1828. He discovered that pressure in veins is significantly lower than pressure in arteries. As a result, he studied liquid flow in small tubes. A few years later he established Poiseuille's Law, which states the resistance, "p," of the flow of blood as "p" = K(L/R[superscript 4]) where L and R are the length and radius of the vessel respectively. K is a positive constant determined by the viscosity of the blood. It is curious that the resistance is inversely proportional to the fourth power of the radius R. At first glance, most individuals may assume the resistance should be inversely proportional to the second power of the radius since the area of a circle is [pi]R[superscript 2]. In this article, mathematics, including finding volume using cylindrical shells, is developed to establish that the resistance is indeed inversely proportional to the fourth power of the radius.