Over Lesson 11–7 A.A B.B C.C D.D 5-Minute Check 1 Find the circumference of the circle to the nearest tenth.

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Presentation transcript:

Over Lesson 11–7 A.A B.B C.C D.D 5-Minute Check 1 Find the circumference of the circle to the nearest tenth.

Splash Screen

Then/Now You have already found the circumference of a circle. (Lesson 11–7) Find areas of circles. Find areas of sectors.

Vocabulary 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

Concept A

Example 1 A Find Areas of Circles A. Find the area of the circle. Round to the nearest tenth. Answer: The area is about square feet. Estimate A ≈ 3 ● 17 2 or 867 A=  r 2 Area of a circle =  ● 17 2 Replace r with 17. =  ● 289Evaluate  ft 2 Use a calculator. Check ≈ 867

Example 1 B 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 ● 4 2 or 48 A=  r 2 Area of a circle =  ● Replace r with =  ● Evaluate (4.15) 2.  54.1 cm 2 Use a calculator. Check 54.1 ≈ 48

A.A B.B C.C D.D Example 1 CYP A A.38.5 m 2 B.44.0 m 2 C m 2 D m 2 A. Find the area of the circle. Round to the nearest tenth.

A.A B.B C.C D.D Example 1 CYP B A.16.3 in 2 B.32.7 in 2 C.84.9 in 2 D in 2 B. Find the area of the circle. Round to the nearest tenth.

Example 2 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.

Example 2 Use Area of Circles to Solve Problems Answer: The area is about 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 –  ● 4 2 Replace ℓ with 18, w with 12, and r with 4. =216 – 16  Simplify.  165.7Use a calculator.

A.A B.B C.C D.D Example 2 CYP A in 2 B in 2 C in 2 D.79 in 2 The rectangular matting for a picture frame has a circular cutout as shown in the figure. What is the approximate area of the matting?

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

Example 3 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 m 2. Replace N with 120 and r with 6. Simplify. Use a calculator.

A.A B.B C.C D.D Example 3 CYP A.4.2 in 2 B.16.8 in 2 C.33.5 in 2 D.66.0 in 2 To the nearest tenth, what is the area of the shaded sector in the circle?

End of the Lesson