Exercise 45 Page 767

We are given the following circle whose circumference is 16π units.

To find the radius of the circle, we use the fact that its circumference is obtained by multiplying two twice the radius with π. C = 2π r ⇒ 16π = 2π r From the equation above, we can get that r=8 units. Therefore, the area of the entire circle is A=8^2π, or 64π units^2. Finally, notice that each shaded area represents one-quarter of the circle.

The total area of the shaded regions is given by the expression below. Shaded Area = 1/4A + 1/4A Let's substitute the area of the circle into the equation above to find the area of the shaded regions.

In conclusion, the total area of the shaded regions is 32π units^2, which tells us that the correct choice is option B.