JAMB 2010 Mathematics · Question 27

An arc subtends an angle of 50º at the center of circle of radius 6cm. Calculate the area of the sector formed

Options

A.100/7
B.80/7
C.110/7
D.90/7

Answer: C. 110/7

Explanation written with AI and checked against the answer key

Analyze the question: We need the area of a sector with central angle 50° and radius 6 cm. Since the options are fractions with denominator 7, the question expects π = 22/7. Concept: Area of sector = (θ/360) × πr² Solution: Area = (50/360) × (22/7) × 6 × 6 Step 1: 6 × 6 = 36, and 36/360 = 1/10, so the 50 becomes 50/10 = 5: Area = 5 × 22/7 = 110/7 cm² Step 2: Check the decimal: 110/7 ≈ 15.71 cm². This is reasonable because the full circle is about 113.1 cm² and 50/360 of that is about 15.7 cm². Answer: The area is 110/7 cm², which is option C. Tip: When the radius is 6 and the angle is a multiple of 10, simplify r²/360 first (36/360 = 1/10). It makes the arithmetic much faster. Also, if the options have 7 in the denominator, use π = 22/7.

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