The area of a sector of a circle of radius 12 cm, formed by an arc of length 7 cm is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 42 cm2.
The length of an arc = θ/360° × 2πR
So, 7 = θ/360° × [2 × π × 12 ]
⇒ 2 × π × 12 × θ = 360 × 7 = 2520
⇒ θ = 2520/24π = 105/π
The area of the sector = θ/360° × πR2
= [π × 122 × (105/π)]/360°
= 42 cm2
Therefore, the area of a sector is 42 cm2.