Question

Use the diagram to answer the questions. What is the area of the circle in terms of pi? π units² What is the measure of the central angle of the shaded sector? ° What is the area of the shaded sector rounded to the nearest whole number? units²

Answer 1

The radius of the circle is 11, so the area is

`A=\pi r^2 = 121\pi`

The central angles of the shaded and non-shaded regions sum up to 360 degrees, so the central angle of the shaded region is

`360-217=143`

The area of the shaded region is in proportion with the area of the whole circle: if the whole area is given by a sector of 360°, the area of a 143° sector will be given by

`A_(360)/ A_(143) = 360/ 143`

Since we know that the whole area is
`121\pi`, we can solve for the area of the 143° sector:

`121\pi/ A_(143) = 360/ 143 \iff A_(143)=(121\pi\cdot 143)/(360) \approx 151`

Answer 2

121

143

151

Explanation: