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Understanding Circle Measurements: Radius, Diameter, and Circumference Calculations

This guide covers essential concepts in circle measurements including calculating the diameter and radius from given measurements, and finding the circumference of circles. It includes step-by-step examples such as determining arc length based on angular measurements. Specifically, you will learn how to simplify calculations and round to the nearest tenth or hundredth. Practice problems are provided for further skill reinforcement, along with exact measures in terms of π. This resource is perfect for students looking to solidify their understanding of circles in geometry.

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Understanding Circle Measurements: Radius, Diameter, and Circumference Calculations

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  1. Warm-UP 14 cm • Find the diameter or radius: a. r = 7 cm; d = ░ b. d = 5 in; r = ░ c. r = 4.2 ft; d = ░ • Simplify (round to the nearest tenth): a. π•20= b. 2•π•7= 2.5 in 8.4 ft 62.8 44.0

  2. Circumference 6.7 Arc Length

  3. Circumference Circumference The distance around a circle

  4. Circumference or

  5. 1. 2. Find the circumference to the nearest tenth. 33 m 14.3 in. C = 89.8 in C = 103.7 m

  6. Exact Measure Circumference EX: What is the exact measure of the circumference? Writing your answer in terms of π 14.3 in.

  7. ON YOUR OWN: What is the exact measure of the circumference? 33 m

  8. 3. The circumference of a half dollar is about 96 millimeters. Find the diameter of the coin to the nearest tenth. d ≈ 30.6 mm

  9. 4. A circular flower garden has a circumference of 20 feet. Find the radius of the garden to the nearest hundredth. r ≈ 3.18 ft

  10. GUIDED PRACTICE 26.9 Simplify (Round to the nearest tenth): 1. 2. 3. 6.3 23.6

  11. Arc Length piece portion a fraction of the circumference of a circle part section

  12. Arc Length Corollary the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360º * *

  13. Guided Practice Complete How Do You Find Arc Length?

  14. A Example 1 90º B 15 ft Find the length of arc AB to the nearest hundredth. A  23.55 ft

  15. Example 2 A 40º B 6 m Find the length of arc AB to the nearest hundredth. A  4.19 m

  16. A 18.84 m Example 3 B 9 m Find the measure of arc AB to the nearest degree. mAB = 120º

  17. A Example 4 1.57 ft 45º B N Find the radius of circle N to the nearest foot. r ≈2 ft

  18. A Example 5 41.87 cm Q 200º B Find the circumference of circle Q. C ≈75.37 cm

  19. Homework p. 226 (1-10, 17-19) Show ALL Work for Credit!!

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