An artery has lost 20% of its diameter due to plaque build up.Determine the percentage reduction in blood flow.

The reduction in blood flow is not directly proportional to the reduction in diameter. Instead, it's related to the cross-sectional area of the artery, which is proportional to the square of the diameter.

Here are the steps to calculate the reduction in blood flow:

1. Calculate the original cross-sectional area of the artery. We can use the formula for the area of a circle, which is πr². However, since we don't have the actual diameter, we can just call this original area A.

2. Calculate the new diameter. If the artery has lost 20% of its diameter, it now has 80% of its original diameter.

3. Calculate the new cross-sectional area with the new diameter. This is (0.8 * r)² * π = 0.64 * r² * π = 0.64A.

4. The reduction in cross-sectional area (and thus blood flow) is the original area minus the new area, which is A - 0.64A = 0.36A.

5. To express this as a percentage, divide by the original area and multiply by 100. So the reduction in blood flow is (0.36A / A) * 100 = 36%.

So, the artery has experienced a 36% reduction in blood flow due to the 20% reduction in diameter.