Example 2 - Find area of sector, radius 4 cm, angle 30 - Examples

 

  1. Chapter 12 Class 10 Areas related to Circles
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Example 2 (Method 1) Find the area of the sector of a circle with radius 4 cm and of angle 30ยฐ. Also, find the area of the corresponding major sector (Use ฯ€ = 3.14). Here, radius = r = 4 cm, ฮธ=30ยฐ Now, Area of sector = ๐œƒ/360ร—๐œ‹๐‘Ÿ2 = 30/360ร—3.14ร—(4)2 = 1/12ร—3.14ร—4ร—4 = 1/3ร—3.14ร—4 = 12.56/3 cm2 = 4.19 cm2 Area of major sector = ((360 โˆ’ ฮธ))/360ร—๐œ‹๐‘Ÿ2 = ((360 โˆ’ 30))/360ร—3.14ร—(4)2 = 330/360ร—3.14ร—4ร—4 = 11/12ร—3.14ร—4ร—4 = 46.05 cm2 Example 2 (Method 2) Find the area of the sector of a circle with radius 4 cm and of angle 30ยฐ. Also, find the area of the corresponding major sector (Use ฯ€= 3.14). Here, radius = r = 4 cm, ฮธ=30ยฐ Now, Area of sector = ๐œƒ/360ร—๐œ‹๐‘Ÿ2 = 30/360ร—3.14ร—(4)2 = 1/12ร—3.14ร—4ร—4 = 1/3ร—3.14ร—4 = 12.56/3 cm2 = 4.19 cm2 Area of major sector = Area of circle โ€“ Area of minor sector Here, radius = r = 4 cm Area of circle = ๐œ‹๐‘Ÿ2 = 3.14 ร— 42 = 3.14 ร— 16 = 50.24 cm2 Area of major sector = Area of circle โ€“ Area of minor sector = 50.24 โ€“ 4.19 = 46.05

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