February 19, 2020
Today's Problem: Biomedical Engineering
Biomedical engineers play a vital role in medical advances and innovations that improve our health and save lives. One application of their work is advancing research into specialized care for patients. This set of problems looks at a recent biomedical invention—artificial hearts for people who suffer from certain forms of heart disease.
3.1) A team of biomedical engineers has constructed a custom artificial heart. The dimensions of this heart are 10 cm by 10 cm by 15 cm and it weighs 480 grams. What is the greatest possible volume of an object with these dimensions for length, width and height, in cubic centimeters?
Use the image below to answer questions 3.2 and 3.3.
3.2) Because artificial hearts differ from natural hearts, engineers must examine and modify Archie’s artificial heart to ensure blood flows throughout his body in an appropriate amount of time. Currently, blood flows out of Archie’s artificial heart and through his large arteries (in purple) at an average rate of 90 cm/second. It slows to 60 cm/second when it reaches his smaller arteries and capillaries (in red). At these average rates, how many seconds, to the nearest hundredth, will it take for blood to travel from his heart at point A to his left hand at point C?
3.3) Using the same rates of blood flow in 3.2, how many seconds, to the nearest hundredth, will it take for blood to travel from Archie’s heart at point D to his right foot at point F?
3.4) A natural heart pumps an average of 2,000 gallons of blood per day. A particular artificial heart can pump an average of 8 liters of blood per minute. If 1 gallon ≈ 3.79 liters, how many more gallons than a natural heart can this artificial heart pump, on average, in a day? Express your answer as a decimal to the nearest tenth.
BAE Systems Engineer Spotlight: Ben Rogers
We’re grateful to BAE Systems, Inc., a patron sponsor of the MATHCOUNTS Foundation, for sponsoring this Future Engineers project! Engineers like Ben make the world a better place and have an impact in their communities. Learn about all of BAE Systems' spotlighted engineers!