OAB is the sector of a circle center O with radius 8 and sector angle 30 BC is perpendicular to OA calculate the area of the shaded region on the diagram
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Given : OAB is the sector of a circle center O with radius 8 and sector angle 30 BC is perpendicular to OA
To Find : area of the shaded region
Solution:
area of the shaded region = Area of Sector OAB - Area of ΔOCB
Area of Sector OAB = (30/360)πR²
= (1/12)π8²
= 64π/12
= 16π/3
= 16.755 cm²
ΔOCB
Sin30° = BC/OB
=> 1/2 = BC/8
=> BC = 4 cm
Cos30° = OC/OB
=> √3 /2 = OC / 8
=> OC = 4√3
Area of ΔOCB = (1/2) * OC * BC
= (1/2) 4√3 * 4
= 8√3
= 13.856 cm²
area of the shaded region = 16.755 - 13.856
= 2.899
= 2.9 cm²
area of the shaded region = 2.9 cm²
Learn More:
find the area of the shaded region in the following figure - Brainly.in
https://brainly.in/question/8104770
https://brainly.in/question/5080554
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