Splash Screen. Lesson Menu Five-Minute Check (over Lesson 11–7) Then/Now New Vocabulary Key Concept: Area of a Circle Example 1: Find Areas of Circles.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 11–7) Then/Now New Vocabulary Key Concept: Area of a Circle Example 1: Find Areas of Circles Example 2: Real-World Example: Use Area of Circles to Solve Problems Key Concept: Area of a Sector Example 3: Find the Area of a Sector

Over Lesson 11–7 5-Minute Check 1 A.50.2 mm B.50 mm C.25.1 mm D.25 mm Find the circumference of the circle to the nearest tenth.

Over Lesson 11–7 5-Minute Check 2 A.37.7 yd B.34.4 yd C.18.8 yd D.18.4 yd Find the circumference of the circle to the nearest tenth.

Over Lesson 11–7 5-Minute Check 3 A.17.1 ft 2 B.17.9 ft C.35.8 ft 2 D.35.8 ft The diameter of a circle is 5.7 feet. Find the circumference of the circle.

Over Lesson 11–7 5-Minute Check 4 A.9.9 in. B.10 in. C.10.1 in. D.10.2 in.

Over Lesson 11–7 5-Minute Check 5 A.12.7 in. B.17.2 in. C.34.6 in. D.35.4 in. What is the approximate circumference of a plate that has a radius of 5.5 inches?

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

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

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.

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.

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

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.

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