A sector of a circle with central angle 120 degrees has an arc length of 8*pi cm. What is the area of the sector?
Answer and explanation
Correct answer: B. 48*pi cm^2
- Step 1: Arc length formula: s = r theta (in radians). 120 degrees = 2pi / 3 radians.
- Step 2: 8pi = r (2pi / 3), so r = 8pi 3 / (2pi) = 12 cm.
- Step 3: Area of sector: A = (1/2) r^2 theta = (1/2) 12^2 (2pi / 3) = (1/2) 144 (2pi / 3) = 48*pi cm^2.
Answer
48*pi cm^2.
Why not the others: 24pi cm^2 computes (1/4)96pi; 96pi cm^2 omits the factor of 1/2; 36*pi cm^2 uses r = 9.
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