geometry section 11-3

Section 11-3Areas of Circles and Sectors

Essential Questions

• How do you find areas of circles?

• How do you find areas of sectors of circles?

Vocabulary

1. Sector of a Circle:

2. Segment of a Circle:

Vocabulary

1. Sector of a Circle: A region of a circle created by an angle whose vertex is the center of the circle (similar to a slice of pie)

2. Segment of a Circle:

Vocabulary

1. Sector of a Circle: A region of a circle created by an angle whose vertex is the center of the circle (similar to a slice of pie)

2. Segment of a Circle: The region of a circle bounded by an arc and a chord

Example 1Fuzzy Jeff Co. 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.

Example 1Fuzzy Jeff Co. 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.

A = π r 2

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

r = 36 + 8

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

r = 36 + 8r = 44 in.

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

r = 36 + 8r = 44 in.

A = π (44)2

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

r = 36 + 8r = 44 in.

A = π (44)2

A = 1936π

Example 1Fuzzy Jeff Co. 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.

A = π r 2 r = 722 + 8

r = 36 + 8r = 44 in.

A = π (44)2

A = 1936π

A ≈ 6082.12 in2

Formula for Area of a SectorA sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle.

Formula for Area of a SectorA sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle.

A = x360 iπ r

2

Formula for Area of a SectorA sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle.

A = x360 iπ r

2

x is the degree of the angle inside the arc

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2 36010

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2 36010

= 36°

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2 36010

= 36°

A = 36360 iπ (4)

2

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2 36010

= 36°

A = 1.6π

A = 36360 iπ (4)

2

Example 2A pumpkin pie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?

A = x360 iπ r

2 36010

= 36°

A = 1.6πA ≈ 5.03 in2

A = 36360 iπ (4)

2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

A = 152360 iπ (7.4)

2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

A = 152360 iπ (7.4)

2

A ≈ 72.64 cm2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

A = 360 − 75360 iπ (4.2)2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

A = 360 − 75360 iπ (4.2)2

A = 285360 iπ (4.2)

2

Example 3Find the area of the shaded sector. Round to the nearest hundredth.

A = x360 iπ r

2

A = 360 − 75360 iπ (4.2)2

A ≈ 43.87 in2

A = 285360 iπ (4.2)

2

Problem Set

Problem Set

p. 784 #1-25 odd

“Nothing is impossible, the word itself says 'I'm possible’!” - Audrey Hepburn