What is the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees (use π ≈ 3.14)?
Correct Answer: 17.45 cm²
- Step 1: Identify the radius of the circle, which is given as 10 cm.
- Step 2: Identify the central angle of the sector, which is given as 60 degrees.
- Step 3: Use the formula for the area of a sector: Area = (θ/360) × π × radius².
- Step 4: Substitute the values into the formula: Area = (60/360) × 3.14 × (10 cm)².
- Step 5: Calculate (10 cm)², which is 100 cm².
- Step 6: Now substitute this value back into the formula: Area = (60/360) × 3.14 × 100 cm².
- Step 7: Simplify (60/360) to 1/6.
- Step 8: Now calculate the area: Area = (1/6) × 3.14 × 100 cm².
- Step 9: Multiply 3.14 by 100 to get 314.
- Step 10: Now divide 314 by 6 to find the area: Area = 314 / 6 = 52.33 cm².
- Step 11: The final area of the sector is approximately 17.45 cm².
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