In cleaning out the artery of a patient, a doctor increases the radius of the opening by a factor of two. By what factor does the cross-sectional area of the artery change?
Isn't area related to the square of radius?
ya i think your right. thank you i got the answer right
To find the factor by which the cross-sectional area of the artery changes, we need to understand the relationship between the radius and the cross-sectional area of a circle.
The cross-sectional area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle.
In this case, the doctor increases the radius of the opening by a factor of two. Let's consider the original radius as r. Then the new radius after the increase is 2r.
Now, let's calculate the cross-sectional area of the artery for both the original and new radii.
For the original radius:
A1 = πr^2
For the new radius:
A2 = π(2r)^2 = π(4r^2) = 4πr^2
To find the factor by which the cross-sectional area changes, we can divide the new area (A2) by the original area (A1):
Factor = A2 / A1 = (4πr^2) / (πr^2) = 4
Therefore, the cross-sectional area of the artery changes by a factor of 4 when the radius of the opening is increased by a factor of two.