Question
Download Solution PDFIn the following figure, the length of arc AB is equal to five times of the radius r of the circle. Find the area of sector AOB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe length of arc AB is equal to five times the radius r of the circle.
Formula used:-
Area of sector = (θ/360) × πr²
Length of arc = (θ/360) × 2πr
Where,
θ is the central angle in degrees
r is the radius of the circle
Calculation:-
The length of arc AB is equal to five times the radius
⇒ 5r = (θ/360) × 2πr
⇒ θ = (5r × 360) / (2πr)
θ = 900 /π degrees
Area of sector = (900/(360× π )) × πr²
Area of sector = 2.5r²
∴The area of sector AOB is 2.5r2.
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