Blood is flowing through an artery of radius 2 mm at a rate of 40 cm/s. Determine the flow rate and the volume that passes through the artery in a period of 30 s.

Video Transcript

This is College Physics Answers with Shaun Dychko. Blood is flowing through an artery of radius two millimeters at a speed of 40 centimeters per second on average. And since this is in units of centimeters per second, we're going to convert the radius into centimeters as well. So that two millimeters times, one centimeter for every 10 millimeters turns into 0.2 centimeters. So the flow rate is the cross-sectional area of the artery times the average velocity of the fluid. So that's PI r squared is the area. And so that's PI times 0.2 centimeters squared times 40 centimeters per second, which is five cubic centimeters per second And in 30 seconds, the question is what volume of blood will pass through the artery. So we have the flow rate is volume per time. It's another way of writing flow rate. And we can solve for V by multiplying both sides by t. We get the volume then as the flow rate times the time. So that's PI r squared average velocity times time. PI times 0.2 centimeters squared times 40 centimeters per second times 30 seconds. Which is two times ten to the two cubic centimeters. And I took only one significant figure here because the radius is given with only one significant figure.