H

Do Now:Read the following definitions:• The length of an arc is the circular distance around the arc.• Let AB be an arc of a circle with center O and radius r. The union of the segments OP (where P is any point on AB) is called a sector. AB is called the arc of the sector, and r is called its radius.

1. Find the exact length of arc AB.

O

A

B450

10 cm

The LENGTH, S, of an arc of a circle with central angle θ and radius r is

S =

O

A

450C

D

B

2. The area of sector AOB is _____ of the circle's area.

b) The area of sector COD is _____ of the circle's area.

1a) The length of AB is ______ of the circumference.

b) The length of CD is _______ of the circumference.

Now, complete the following:

A

BOsector

length

900

S

10

2. Find the length of the minor arc.

CC Geometry HAim #12: How do we find the length of an arc and area of a sector of a circle?

5. P and Q are points on the circle of radius 5 cm, and the measure of arc PQ is 72°. Find, to one decimal place, each of the following.

a. the length of PQ

b. the ratio of the exact arc length to the radius of the circle

4. Find the length of an arc intercepted by a central angle of 300 if the radius of the circle is 12 cm. Leave π in your answer.

3. Find the degree measure of an arc whose length is 3π and is part of a circle that has a radius of 12.

=AS AREA OF A SECTOR (As) of a circle with central angle θ

6. Find the area of sector AOB.

O

A

B450

10 cm

91200

8. Find the area of the sector, in terms of π.

9. Find the area of the sector, in terms of π.

Mixed Practice

7. If the radius of a circle is 10 and the area of a sector is 10π, what is the measure of the central angle?

10. Find the area of a sector of a circle with a central angle of 300. The radius of the circle is 10 cm. Leave π in your answer.

11. Find the length of an arc intercepted by a central angle of 60o. The radius of the circle is 18 m. Leave π in your answer.

12. Find the area of a sector of a circle with a central angle of 45o. The diameter of the circle is 16 cm. Leave π in your answer.

120 0

A

B

O

13. Find the length of AB to the nearest tenth. AO = 24 cm.

15. In the circle given, ED is the diameter and is perpendicular to chord CB. DF = 8 cm and FE = 2 cm. Find AC, BC, m≮CAB, the length of CEB, and the area of sector CAB (round to the nearest hundredth, if necessary).

14. The area of a circle is 625π. If a sector of the circle has an angle of 72o, find the area of the sector in terms of π.

Name: _____________________ CC Geometry HDate: ____________ HW #12

2) a. Find the arc length of PQR.

b. Find the area of sector POR.

3. What is the radius of a circle if the length of a 45° arc is 9π?

45°

4. Given circle A, find the following (round to the nearest hundredth, if necessary).

a. circumference of circle A

b. radius of circle A

c. area of sector CAD

1. P and Q are points on the circle of radius 5 cm, and the measure of arc PQ is 72°. Find, to one decimal place, each of the following.

a. the length of PQ

b. the area of sector POQ

6. In the figure, if PQ = 10 cm, find the length of QR .

7. Find the area of the entire circle given the area of the sector.

5. A circle is divided into 6 equal sections by points A, B, C, D, E, and F. If its radius is 15 cm., find the length of CD to the nearest tenth.

8. AB and CD both have an angle measure of 30°, but their arc lengths are not the same. OB = 4 and BD = 2.a. What are the arc lengths of AB and CD?

b. What is the ratio of the arc length to the radius for both of these arcs? Explain.

c. What are the areas of the sectors AOB and COD?

Review9. The diameter of a soccer ball is approximately 22 cm, and the diameter of a baseball is approximately 75 mm. The volume of the soccer ball is how many times greater than the volume of the baseball, to the nearest integer?