Chapter 8 Areas of Polygons and Circles Copyright
- Slides: 15
Chapter 8 Areas of Polygons and Circles Copyright © Cengage Learning. All rights reserved.
8. 4 Circumference and Area of a Circle Copyright © Cengage Learning. All rights reserved.
Circumference and Area of a Circle Theorem 8. 4. 1 The circumference of a circle is given by the formula C = d or C = 2 r 3
Value of When a calculator is used to determine with greater accuracy, we see an approximation such as = 3. 141592654. 4
Example 1 In O in Figure 8. 41, OA = 7 cm. Using a) find the approximate circumference C of O. b) find the approximate length of the minor arc . Solution: a) C = 2 r = = 44 cm Figure 8. 41 5
Example 1 – Solution cont’d b) Because the degree of measure of is 90 , the arc length is of the circumference, 44 cm. Thus, length of = 6
LENGTH OF AN ARC 7
Length of an Arc Informally, the length of an arc is the distance between the endpoints of the arc as though it were measured along a straight line. Two further considerations regarding the measurement of arc length follow. 1. The ratio of the degree measure m of the arc to 360 (the degree measure of the entire circle) is the same as the ratio of the length ℓ of the arc to the circumference; that is, 8
Length of an Arc 2. Just as m denotes the degree measure of an arc, ℓ denotes the length of the arc. Whereas m is measured in degrees, ℓ is measured in linear units such as inches, feet, or centimeters. 9
Length of an Arc Theorem 8. 4. 2 In a circle whose circumference is C, the length ℓ of an arc whose degree measure is m is given by Note: For arc AB, 10
Example 4 Find the approximate length of major arc ABC in a circle of radius 7 in. if = 45. See Figure 8. 43. Use . Figure 8. 43 11
Example 4 – Solution According to Theorem 8. 4. 2, or which can be simplified to 12
AREA OF A CIRCLE 13
Area of a Circle Theorem 8. 4. 3 The area A of a circle whose radius has length r is given by A = r 2. 14
Example 6 Find the approximate area of a circle whose radius has a length of 10 in. Use 3. 14. Solution: A = r 2 becomes A = 3. 14(10)2. Then A = 3. 14(100) = 314 in 2 15
- Developing formulas for circles and regular polygons
- 10-2 developing formulas for circles and regular polygons
- Developing formulas for circles and regular polygons
- 9-2 developing formulas for circles and regular polygons
- 10-2 developing formulas for circles and regular polygons
- Developing formulas for circles and regular polygons
- Area of polygons and circles
- Differentiate similar polygons from congruent polygons
- 11-3 areas of circles and sectors answer key
- Area of circles and sectors
- Lesson 11-3 areas of circles and sectors
- Areas of circles and sectors practice
- Circumferences and areas of circles 11-5
- 11-4 areas of regular polygons
- 11-4 area of regular polygons
- Circle theorem