### Home > MC2 > Chapter 8 > Lesson 8.2.4 > Problem8-70

8-70.

In the circle at right, the shaded sector is $\frac { 1 } { 8 }$ of the circle.

1. What is the area of the unshaded region of the circle? Write your answer in terms of $π$ and as a decimal approximation.

If the unshaded region were half of the circle, then its area would be half that of the entire circle.
Begin by determining what portion of the circle is unshaded and by finding the circle's total area.

Area of a circle $= π · r^2 = 25$?
If $\frac{1}{8}$ of the circle is shaded, what fraction is unshaded?

$\frac{175}{8} \pi \approx$ $68.72$ square inches

2. What is the area of the shaded region? Write your answer in terms of $π$ and as a decimal approximation.

See part (a).

What is $\frac{1}{8}$ of the total area of the circle $(25\pi)$?

3. In a few sentences explain each of the steps you followed to answer parts (a) and (b).

What strategy did you use to solve for parts (a) and (b)?
Describe how you were able to find the area of the various portions of the circle.