Question

problem 2. (hold the mayo!) coronary arteries are responsible for supplying oxygenated blood to heart muscle. coronary heart disease is caused by the arteriosclerosis (the deposition of plaque along the arterial walls). one common response by the body to coronary arteriosclerosis is to increase the blood pressure which can cause damage to the body's organs if too high. we will analyze the scenario of constriction of an artery where damping effects cannot be ignored. a. the radius of a typical open artery is 1.5 mm. what is the radius of an artery that is 33% occluded? (33% of the cross-sectional area is taken up by plaque.) give your answer in mm.

Answer 1

To calculate the radius of an artery that is 33% occluded, we can compare the cross-sectional areas of the open artery and the occluded artery.

The formula A = πr^2 is used to calculate the cross-sectional area, and the formula r = sqrt(A/π) is used to calculate the radius.

Using these formulas, we find that the radius of the occluded artery is 1.22 mm.

Step-by-step explanation:

The radius of an artery that is 33% occluded can be calculated by comparing the cross-sectional areas of the open artery and the occluded artery.

In this case, the radius of the open artery is given as 1.5 mm. We can calculate the cross-sectional area of the open artery using the formula A = πr^2, where A is the area and r is the radius.

So, for the open artery, the area is:

A = π(1.5^2)

= 7.07 mm^2.

If the occluded artery has 33% of its cross-sectional area taken up by plaque, then the remaining area is 67%.

We can calculate the radius of the occluded artery using the formula r = sqrt(A/π), where r is the radius and A is the area.

So, for the occluded artery, the radius is:

r = sqrt(0.67 x 7.07/π)

= 1.22 mm.

Therefore, the radius of an artery that is 33% occluded is 1.22 mm.