The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector. $(Take \pi = \frac{22}{7})$

Analyze the question: We need the area of a sector with radius r = 3.4 cm and angle θ = 115°, using π = 22/7.

Concept: Area of a sector = (θ/360) × πr²

Solution:

1. Compute r²: 3.4² = 11.56

2. Compute πr²: (22/7) × 11.56 = 254.32/7 ≈ 36.331

3. Multiply by the fraction of the circle: 115/360 = 23/72 ≈ 0.31944

Area = 0.31944 × 36.331 ≈ 11.606 cm²

Rounded to 1 decimal place, the area is about 11.6 cm².

Checking the other options: 12.7, 10.2 and 9.4 do not match 11.606, so they are ruled out.

Tip: In sector questions, simplify the angle fraction first (115/360 = 23/72) and estimate before calculating. Here the full circle is about 36.3 cm², and 115° is a little less than one third of 360°, so the answer should be a little under 12. That quickly points to 11.6 and away from the other options.