1. Section 11.3 Notes: Areas of Circles and Sectors
Students will be able to find areas of circles.
Students will find areas of sectors of circles.

2. In Lesson 10-1, you learned that the formula for the circumference C of a circle with radius r is given by 𝐶=2𝜋𝑟. You can use this formula to develop the formula for the area of a circle.
Below, a circle with radius r and circumference C has been divided into congruent pieces and then rearranged to form a figure that resembles a parallelogram.

3. Vocabulary!
Area of a Circle

4. Example 1:
Example 1: An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.

5. Example 2:
Example 2: Find the radius of a circle with an area of 58 square inches.

6. Vocabulary! Sector* Area of a Sector
*Add to workbook
A region of a circle bounded by a central angle and its intercepted major or minor arc.
Area of a Sector   
The ratio of the area of a sector to the area of the
whole circle, is equal to the ratio of the degree measure
of the intercepted arc to 360.

7. Example 3:
a) A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth?

8. Example 3:
b) A pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth?

9. You Try!
a) Find the area of the shaded sector. Round to the nearest tenth

10. You Try!
b) Find the area of the shaded sector. Round to the nearest tenth

11. Extra Practice:
Calculate the sector area: a.

12. Extra Practice:
b. Calculate the sector area:

13. Extra Practice:
c. Calculate the sector area:

14. 2) The area of a circle is 225π square inches
2) The area of a circle is 225π square inches. Find the area of the sector whose central angle is 45˚.

15. 3) The central angle of a sector is 60˚ and the area of the circle is 144π. What is the area of the sector?

16. 4) A circle has a radius of 12
4) A circle has a radius of 12. Find the area of the sector whose central angle is 120˚.

17. 5) Find the radius of a circle which has a sector area of 9π whose central angle is 90˚.

18. Example 9:
6)The central angle of a sector is 72˚ and the sector has an area of 5π. Find the radius.

19. 7) Find the measure of the central angle of a sector if its area is 5π and the radius is 6.

20. 8) If the area of a circle is 254 m2, find the circumference
8) If the area of a circle is 254 m2, find the circumference. Round to the nearest tenth.

21. 9) Find if the area of the sector is 11. 2 ft2
9) Find if the area of the sector is 11.2 ft2. Round to the nearest degree.

22. 10. Find the radius of the circle if the area of the shaded region is 78.3 ft2. Round to the nearest tenth.

23. 11. Find the exact area of the shaded region.

24. 12. Find the area of the shaded region. Round to the nearest hundredth.

25. Written Summary!
Helping You Remember: A good way to remember something is to explain it to someone else. Suppose Jimmy is having trouble remembering which formula is for circumference and which is for area. How can you help him out?