The document provides examples and problems related to calculating the areas of circles. It includes examples of estimating areas using approximations of π, finding areas using the exact formula, and word problems involving circle areas. Sample problems are provided to estimate or calculate the areas of various circles.

1. Warm Up Lesson Presentation Problem of the Day Lesson Quizzes

2. Warm Up Evaluate. 1. 6  4 2 2. 5.6  2 3 Simplify each expression. 3. 6 + n – 4 4. 5( n + 1) 96 44.8 n + 2 5 n + 5

3. Problem of the Day What is the area of a right triangle with legs measuring 31 in. and 21 in.? 325.5 in 2

4. MA.6.A.4.1 …Estimate and calculate…the area of circles. Also MA.6.A.3.4 Sunshine State Standards

6. Additional Example 1A: Estimating the Area of a Circle Estimate the area of the circle. Use 3 to approximate  . A =  r 2 Write the formula for area. Replace  with 3 and r with 20 . Use the order of operations. Multiply. A ≈ 3 • 20 2 A ≈ 1,200 m 2 A ≈ 3 • 400

7. Additional Example 1B: Estimating the Area of a Circle Estimate the area of the circle. Use 3 to approximate  . A =  r 2 Write the formula for area. Replace  with 3 and r with 14 . Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. Multiply. r = 28 ÷ 2 A ≈ 3 • 14 2 r = 14 A ≈ 3 • 196 A ≈ 588 ft 2

8. Check It Out: Example 1A Estimate the area of the circle. Use 3 to approximate  . A =  r 2 Write the formula for area. Replace  with 3 and r with 25 . Use the order of operations. Multiply. A ≈ 3 • 25 2 A ≈ 1,875 m 2 24.8 m A ≈ 3 • 625

9. Check It Out: Example 1B Estimate the area of the circle. Use 3 to approximate  . 20 m A =  r 2 Write the formula for area. Replace  with 3 and r with 10 . Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. Multiply. r = 20 ÷ 2 A ≈ 3 • 10 2 r = 10 A ≈ 3 • 100 A ≈ 300 m 2

10. Additional Example 2A: Using the Formula for the Area of a Circle Find the area of the circle. Use for  . Write the formula to find the area. A =  r 2 The length of the diameter is twice the length of the radius. Use the order of operations. A  50 ft 2 Divide. 22 7 2 7 r = d ÷ 2 r = 8 ÷ 2 = 4 Replace  with and r with 4 . 22 7 __ A  • 16  22 7 __ A  • ( 4 ) 2 22 7 352 7

11. Additional Example 2B: Using the Formula for the Area of a Circle Find the area of the circle. Use for  . Write the formula to find the area. A =  r 2 Use the GCF to simplify. 7 A  154 cm 2 Multiply. 22 7 1 Replace  with and r with 7 . 22 7 __ A  • 49 22 7 __ A  • 7 2 22 7

12. Write the formula to find the area. A =  r 2 The length of the diameter is twice the length of the radius. Use the GCF to simplify. 28 A  616 cm 2 Multiply. Check It Out: Example 2A Find the area of the circle. Use for  . 22 7 1 28 cm r = d ÷ 2 r = 28 ÷ 2 = 14 Replace  with and r with 14 . 22 7 __ A  • 196 22 7 __ A  • 14 2 22 7

13. Check It Out: Example 2B Find the area of the circle. Use for  . Write the formula to find the area. A =  r 2 Use the GCF to simplify. 7 A  154 cm 2 Multiply. 22 7 1 7 cm Replace  with and r with 7 . 22 7 __ A  • 49 22 7 __ A  • 7 2 22 7

14. Additional Example 3: Application A drum head has a radius of 18 in. Find the area of the material covering the drum head. use 3.14 for  . 18 in. A =  r 2 Write the formula for area. Replace  with 3.14 and r with 18 . Use the order of operations. Multiply. A  3.14 • 18 2 A  3.14 • 324 A  1,017.36 in 2

15. Additional Example 3 Continued A drum head has a radius of 18 in. Find the area of the material covering the drum head. use 3.14 for  . 18 in. Check Use 3 as an estimate for  . The area,  r 2 , is approximately 3 • 18 2 = 3 • 324 = 972, so the answer is reasonable.

16. 18 m A =  r 2 Write the formula for area. Replace  with 3.14 and r with 9 . Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. Multiply. Check It Out: Example 3 A cymbal has a diameter of 18 in. Find its area. Use 3.14 for  . r = 18 ÷ 2 A  3.14 • 9 2 r = 9 A  3.14 • 81 A  254.34 m 2

17. Check It Out: Example 3 Continued A drum head has a radius of 18 in. Find its area. Use 3.14 for  . Check Use 3 as an estimate for  . The area,  r 2 , is approximately 3 • 9 2 = 3 • 81 = 243, so the answer is reasonable. 18 m

18. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Lesson Quiz: Part I Estimate the area of each circle. 1. 2. 27 km 2 1,200 yd 2

20. 3. 4. 4.53 cm 2 1.54 m 2 Lesson Quiz: Part II Find the area of each circle. Use for  . 22 7 5. A coaster has a diameter of 6 inches. Find the area of the largest circular cup base the coaster can hold. Use 3.14 for  . 28.26 in 2

21. 1. Estimate the area of the circle. Use 3 for  . A. 48 km 2 B. 46 km 2 C. 44 km 2 D. 42 km 2 Lesson Quiz for Student Response Systems 4 km

22. 2. Estimate the area of the circle. Use 3 for  . A. 772 yd 2 B. 872 yd 2 C. 972 yd 2 D. 992 yd 2 Lesson Quiz for Student Response Systems 36 yd

23. 3. Estimate the area of the circle. Use 3 for  . A. 36.75 cm 2 B. 21 cm 2 C. 10.5 cm 2 D. 9.19 cm 2 Lesson Quiz for Student Response Systems 3.5 cm

24. 4. A circular table has a diameter of 8 feet. Identify the area of the table cloth needed to cover the table. Use 3.14 for  . A. 25.12 ft 2 B. 37.68 ft 2 C. 40.82 ft 2 D. 50.24 ft 2 Lesson Quiz for Student Response Systems