Too much cholesterol is a health risk because fatty deposits build up in arteries. the lumen of an artery had a diameter of 5.0mm before the build-up of a fatty deposit. the fatty deposit covers 65% of the original area of the lumen. calculate the area in mm² of the lumen that is available for blood flow. [area of the lumen = r 2 ] [π=3.14]
The radius of the original lumen is:
r = d/2 = 5.0mm/2 = 2.5mm
The area of the original lumen is:
A = πr^2 = 3.14 x (2.5mm)^2 = 19.625mm²
The fatty deposit covers 65% of the original area, so the available area for blood flow is:
A_available = (100% - 65%) x A = 35% x 19.625mm² = 6.857mm²
Therefore, the area in mm² of the lumen that is available for blood flow is approximately 6.857mm².