Find the area of a minor sector of a circle whose circumference is 88 cm and the length of its minor arc is 22 cm (use π = 22/7)
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 154 cm2.
Circumference of the circle = 2π(radius) = 88 cm
⇒ 2πr = 88
⇒ 2 × (22/7) × r = 88
⇒ r = 14 cm
Length of the minor arc = 2πr × (θ/360) = 22 cm
⇒ 2πr × (θ/360) = 22
⇒ 88 × (θ/360) = 22
⇒ θ = 360/4 = 90°
Area of the minor sector of the circle = πr2 × (θ/360) = (22/7) × 14 × 14 × (90/360) = 44 × 14 × (1/4) = 11 × 14 = 154 cm2