What is the area of a sector of a circle with a radius of 4 m and a central angle of 90 degrees?

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Q: What is the area of a sector of a circle with a radius of 4 m and a central angle of 90 degrees?

Solution: Area of sector = (θ/360) × πr² = (90/360) × π × (4 m)² = (1/4) × 3.14 × 16 m² = 12.56 m².

Steps: 11

Step 1: Identify the radius of the circle, which is given as 4 meters.
Step 2: Identify the central angle of the sector, which is given as 90 degrees.
Step 3: Use the formula for the area of a sector: Area = (θ/360) × πr².
Step 4: Substitute the values into the formula: Area = (90/360) × π × (4 m)².
Step 5: Calculate (4 m)², which is 16 m².
Step 6: Now substitute this value back into the formula: Area = (90/360) × π × 16 m².
Step 7: Simplify (90/360) to (1/4).
Step 8: Now the formula looks like this: Area = (1/4) × π × 16 m².
Step 9: Multiply (1/4) by 16 m², which equals 4 m².
Step 10: Now multiply 4 m² by π (approximately 3.14): Area = 4 m² × 3.14.
Step 11: Calculate the final area: Area ≈ 12.56 m².