Over Lesson 11–7

A. A

B. B

C. C

D. D

Find the circumference of the circle to the nearest tenth.

Find the circumference of the circle to the nearest tenth.

You have already found the circumference of a circle. (Lesson 11–7)

• Find areas of circles.

• Find areas of sectors.

• sector

• central angle

A pie-shaped part of a circle bound by the radius of a circle and an arc

An angle whose vertex is the center of the circle and whose sides are radii

Find Areas of Circles

A. Find the area of the circle. Round to the nearest tenth.

Answer: The area is about 907.9 square feet.

Estimate A ≈ 3 ● 172 or 867

A = r 2 Area of a circle

= ● 172 Replace r with 17.

= ● 289 Evaluate 172.

907.9 ft2 Use a calculator.

Check 907.9 ≈ 867

Find Areas of Circles

B. Find the area of the circle. Round to the nearest tenth.

Answer: The area is about 54.1 square centimeters.

Estimate A ≈ 3 ● 42 or 48

A = r 2 Area of a circle

= ● 4.152 Replace r with 4.15.

= ● 17.2225 Evaluate (4.15)2.

54.1 cm2 Use a calculator.

Check 54.1 ≈ 48

A. A

B. B

C. C

D. D

A. 38.5 m2

B. 44.0 m2

C. 153.9 m2

D. 615.8 m2

A. Find the area of the circle. Round to the nearest tenth.

A. A

B. B

C. C

D. D

A. 16.3 in2

B. 32.7 in2

C. 84.9 in2

D. 339.8 in2

B. Find the area of the circle. Round to the nearest tenth.

Use Area of Circles to Solve Problems

PICTURE FRAMES The rectangular matting for a picture frame has a circular cutout for the photograph, as shown in the figure. What is the area of the mat? Round to the nearest tenth.

Use Area of Circles to Solve Problems

Answer: The area is about 165.7 sq. in.

Find the area of the rectangle minus the area of the circle.

Area of rectangle Area of circle

A = ℓw – r 2

= 18 ● 12 – ● 42 Replace ℓ with 18, w with12, and r with 4.

= 216 – 16 Simplify.

165.7 Use a calculator.

A. A

B. B

C. C

D. D

A. 150.6 in2

B. 131.7 in2

C. 124.6 in2

D. 79 in2

The rectangular matting for a picture frame has a circular cutout as shown in the figure. What is the approximate area of the matting?

This is tells you how big of a pie slice you are “cutting”

Find the Area of a Sector

Find the area of the shaded sector in the circle. Round to the nearest tenth.

Area of a sector

Answer: The area is about 37.7 m2.

Replace N with 120 and r with 6.

Simplify.

Use a calculator.

A. A

B. B

C. C

D. D

A. 4.2 in2

B. 16.8 in2

C. 33.5 in2

D. 66.0 in2

To the nearest tenth, what is the area of the shaded sector in the circle?