Question
Download Solution PDFIn the given figure, the length of arc AB is equal to 3 times radius r of the circle.
Find the area of sector OAB in terms of radius r.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
Area of an arc = θ/360 × πr2 .
θ = arc / radius
1 radian = 180°/π
Calculation:
Here the arc = 3r
So, θ = 3r / r
⇒ 3c
We know,
πc = 180°
3c = (180/π × 3) = 540/π degree
So, angle in degree (θ) = (540/π) degree
The area of the sector OAB is,
⇒ (540/π)/360 × πr2
⇒ 540/360 × r2 = 3/2 r2 = 1.5 r2
∴ The area of the sector OAB is 1.5 r2.
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