Perimeter of a sector
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The document discusses calculating the perimeter of a sector of a circle. It defines a sector as an arc with two radii extending from the endpoints of the arc. The perimeter of a sector is the sum of the length of the arc and the two radii. Several examples are provided of calculating perimeters of sectors given the central angle, radius, or other information about the sector.
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Perimeter of a sector
- 2. Sector of a Circle The sector of a circle is a part of the circle made up of an arc along with two radii which are at the end points of the arc. The diagram shows a circle divided into two sectors; a major sector and a minor sector.
- 3. Perimeter of a sector of a circle RECALL: Perimeter is the distance around a figure. The perimeter of a sector would be the sum of the length of the arc, and the two radii. 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠
- 4. RECALL: Length of an Arc
- 5. EXAMPLE: Use 𝜋 = 22 7 . Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 64 360 × 2 × 22 7 × 5.5 + (2 × 5.5) = 𝟏𝟕. 𝟏 𝒎 Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 197 360 × 2 × 22 7 × 7.7 + (2 × 7.7) = 𝟒𝟏. 𝟗 𝒎𝒎
- 6. EXAMPLE: Use 𝜋 = 22 7 . Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 284 360 × 2 × 22 7 × 3.6 + (2 × 3.6) = 𝟐𝟓 𝒎𝒎 Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 126 360 × 2 × 22 7 × 4.8 + (2 × 4.8) = 𝟐𝟎. 𝟐 𝒄𝒎
- 7. EXAMPLE: Use 𝜋 = 22 7 . Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 275 360 × 2 × 22 7 × 9 + (2 × 9) = 𝟔𝟏. 𝟐 𝒄𝒎 Calculate the perimeter: 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠) = 249 360 × 2 × 22 7 × 9.2 + (2 × 9.2) = 𝟓𝟖. 𝟒 𝒎
- 8. Example Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠 = 60 360 × 2 × 22 7 × 28 + 28 + 28 ` = 85.3 𝑚 A plot of land is in the shape of a sector of a circle of radius 28 m. If the sectorial angle (central angle) is 60°, find the perimeter of the plot. (𝑈𝑠𝑒 𝜋 = 22 7 . )
- 9. Example Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠 30 = 16 + 2𝑟 ` 2𝑟 = 30 − 16 = 14 𝑟 = 7 𝑐𝑚 Find the radius of sector whose perimeter is 30 cm and length of the arc is 16 cm.
- 10. Example Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠 45 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 10 + 10 45 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 20 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 = 45 − 20 = 25 𝑐𝑚 Find the length of arc, if the perimeter of the sector is 45 cm and the radius is 10 cm.
- 11. THE END.
Editor's Notes
- NOTE: To change the image on this slide, select the picture and delete it. Then click the Pictures icon in the placeholder to insert your own image.