What is the area of a sector of a circle with a radius of 4 m and a central angle of 90 degrees? (Use π = 3.14)

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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? (Use π = 3.14)

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

Steps: 10

Step 1: Identify the radius of the circle. In this case, the radius (r) is 4 meters.
Step 2: Identify the central angle of the sector. Here, the angle (θ) is 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. We have θ = 90 degrees, π = 3.14, and r = 4 m.
Step 5: Calculate r² (the radius squared). 4 m × 4 m = 16 m².
Step 6: Now substitute r² into the formula: Area = (90/360) × 3.14 × 16 m².
Step 7: Simplify the fraction 90/360. This equals 1/4.
Step 8: Now the formula looks like this: Area = (1/4) × 3.14 × 16 m².
Step 9: Calculate (1/4) × 16 m², which equals 4 m².
Step 10: Finally, multiply 4 m² by 3.14 to get the area: 4 m² × 3.14 = 12.56 m².