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Understanding Circle Measurements: Circumference and Area Calculations

This guide covers the fundamental concepts of finding the circumference and area of circles. Learn how to calculate the circumference of a circle from its diameter or radius and how to round your results accurately. We also explore finding the radius from a known circumference. Examples and exercises on sectors and shaded areas will enhance your understanding of these geometric principles. Practice problems help reinforce learning through real-world applications involving circle measurements.

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Understanding Circle Measurements: Circumference and Area Calculations

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  1. Warm-Up • Find the circumference of a circle with a diameter of 10ft. Round your answer to the nearest tenth. • Find the circumference of A if the radius is 2.5. Round your answer to the nearest hundredth. • Find the radius of a circle with a circumference of 56.5 m. 31.4 ft 15.71 8.99 m

  2. Review Info.(what we learned yesterday) Circumference: (distance around the circle) OR Arc length=

  3. Continued from yesterday: Your Turn: Find the circumference of circle C. A 200o C 41.87 cm B

  4. Your Turn: Find the radiusof circle C.READ the directions carefully!!! R 1.57 ft S 45o C

  5. r Area A= pr2 The amount of space occupied.

  6. 53 cm 7.6 yd Find the area. 181.5 square yards 2206.2 square cm

  7. A= pr2 Example 1 C = 2pr A= p 52 10p= 2pr A= p 25 If S has a circumference of 10p inches, find the area of the circle to the nearest hundredth. 5= r A= 78.54 in2

  8. A= p22 A= p82 A= p4 A= p64 A= 12.57in2 A= 201.06in2 A shaded= A – A= 201.06 - 12.57 = Example 2 2 in 6 in Find the area of the shaded region. 188.49in2

  9. Sector the region bounded by two radii of the circle and their intercepted arc.

  10. Area of a Sector

  11. R 6 cm 60 Example 3 Q Find the area of the sector. A  18.85 cm2

  12. 6 cm 7 cm R Q 120 Example 4 Find the area of the sector. A  51.31 cm2

  13. 6 cm r cm R A = 96.8 Q Example 5 mArc = 110 Find the radius if the area of the sector is 96.8. r  10

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