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Understanding Circumference and Area of Circles: A Comprehensive Guide

This lesson focuses on finding the circumference and area of circles using formulas and examples. Learn how to calculate the circumference using both the diameter and radius, applying the formulas C = πd and C = 2πr. Discover how to determine the area with A = πr². Through step-by-step examples, you will practice these calculations, rounding results to the nearest tenth. Topics include finding various circle measurements, and practical applications such as calculating the area of walkways around circular pools.

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Understanding Circumference and Area of Circles: A Comprehensive Guide

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  1. Find the circumference and area of circles. • circle • center • radius • diameter • circumference • pi Lesson 1 MI/Vocab

  2. Lesson 1 Key Concept 1

  3. ×  Use a calculator to find 5. 5 15.70796327 ENTER = Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. C = d Circumference of a circle C = 5Replace d with 5. C = 5 This is the exact circumference. Answer: The circumference is about 15.7 feet. Lesson 1 Ex1

  4. Find the circumference of the circle. Round to the nearest tenth. • A • B • C • D A. 38.5 in. B. 31.4 in. C. 22.0 in. D. 19.7 in. Lesson 1 CYP1

  5. Find the Circumferences of Circles Find the circumference of the circle. Round to the nearest tenth. C = 2r Circumference of a circle C = 2  3.8 Replace r with 3.8. C ≈ 23.9 Use a calculator. Answer: The circumference is about 23.9 meters. Lesson 1 Ex2

  6. Find the circumference of the circle. Round to the nearest tenth. • A • B • C • D A. 9.4 m B. 11.3 m C. 18.5 m D. 22.6 m Lesson 1 CYP2

  7. Lesson 1 Key Concept 2

  8. Find the Areas of Circles Find the area of the circle. Round to the nearest tenth. A = r2 Area of a circle A =   32 Replace r with 3. A =   9 Evaluate 32. A ≈28.3 Use a calculator. Answer: The area is about 28.3 square yards. Lesson 1 Ex3

  9. Find the area of the circle. Round to the nearest tenth. • A • B • C • D A. 12.6 ft2 B. 14.1 ft2 C. 15.3 ft2 D. 17.4 ft2 Lesson 1 CYP3

  10. Find the Areas of Circles Find the area of the circle. Round to the nearest tenth. A = r2 Area of a circle A =   52 Replace r with half of 10 or 5. A =   25 Evaluate 52. A ≈78.5 Use a calculator. Answer: The area is about 78.5 square inches. Lesson 1 Ex4

  11. Find the area of the circle. Round to the nearest tenth. • A • B • C • D A. 42.7 cm2 B. 50.3 cm2 C. 52.1 cm2 D. 54.6 cm2 Lesson 1 CYP4

  12. POOLSThe Patels have a circular pool with a radius of 12 feet. They plan on installing a 4-foot-wide walkway around the pool. What will be the area of the walkway? To determine the area of the walkway, you must subtract the area of the pool from the area of the outer circle that includes the pool and the walkway. Lesson 1 Ex5

  13. Area of Outer Circle A = r2 Area of a circle A = (16)2 Replace r with 12 + 4 or 16. A =   256 Evaluate 162. Lesson 1 Ex5

  14. Area of Pool A = r2 Area of a circle A =  122 Replace r with 12. A =   144 Evaluate 122. Lesson 1 Ex5

  15. Area of Walkway = Area of Outer Circle – Area of Pool ≈ 256 – 144 ≈ 351.9 Answer: The area of the walkway is about 351.9 square feet. Lesson 1 Ex5

  16. POOLS The Shoemakers have a circular pond with a radius of 4 feet. They plan on installing a 2-foot-wide walkway around the pond. What will be the area of the walkway? • A • B • C • D A. 62.8 ft2 B. 84.3 ft2 C. 99.2 ft2 D. 113.1 ft2 Lesson 1 CYP5

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