Question

In cleaning out the artery of a patient, a doctor increases the radius of the opening by a factor of 2.0 By what factor does the cross-sectional area of the artery change?

Short answer

Answer: 4

Step-by-step solution

1. Write down the original radius of the artery and the new radius

Let the original radius be R and the increased radius be 2R, since it is increased by a factor of 2.

2. Calculate the original cross-sectional area

Using the formula A=πR^2, we can calculate the original cross-sectional area as A1 = πR^2.

3. Calculate the new cross-sectional area with the increased radius

With the increased radius of 2R, we can calculate the new cross-sectional area as A2 = π(2R)^2.

4. Calculate the factor by which the area changes

To find the factor by which the area changes, we can divide the new area by the original area. So, the factor is given by: Factor = A2 / A1 Factor = (π(2R)^2) / (πR^2)

5. Simplify the expression

By simplifying the expression, we get: Factor = (4πR^2) / (πR^2) Factor = 4 By increasing the radius of the artery by a factor of 2, the cross-sectional area of the artery changes by a factor of 4.