Question

part d
some forms of cardiovascular disease involve the buildup of plaque on the inside walls of blood vessels. the buildup can put added stress on the heart and vessels, reducing or preventing blood flow to vital organs of the body.
imagine that the diagram is a circular cross - section of a blood vessel. what is the area of the inside of the blood vessel (i.e., the yellow part) in square units? round your answer to the nearest tenth. the equation for the area of a circle is a = πr², where a is area, π = 3.14, and r is the radius. recall that the radius is half of the diameter.

part e
imagine that plaque uniformly coats the walls of the blood vessel in the diagram. based on the diagram, what is the reduced area inside the blood vessel? round your answer to the nearest tenth. the equation for the area of a circle is a = πr², where a is area, π = 3.14, and r is the radius. recall that the radius is half of the diameter.

Explanation:

Step1: Find radius for Part D

Given diameter $d = 7$, radius $r=\frac{d}{2}=\frac{7}{2}=3.5$.

Step2: Calculate area for Part D

Using formula $A=\pi r^{2}$, with $\pi = 3.14$ and $r = 3.5$, we have $A=3.14\times3.5^{2}=3.14\times12.25 = 38.465\approx38.5$.

Step3: Find radius for Part E

Given diameter of reduced - area circle $d = 4$, radius $r=\frac{d}{2}=2$.

Step4: Calculate reduced area for Part E

Using formula $A=\pi r^{2}$, with $\pi = 3.14$ and $r = 2$, we have $A=3.14\times2^{2}=3.14\times4 = 12.6$.

Answer:

Part D: $38.5$ square units
Part E: $12.6$ square units