What is the area of a sector of a circle with a radius of 6 cm and a central ang

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Question: What is the area of a sector of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14)

Options:

Correct Answer: 18.84 cm²

Solution:

Area = (θ/360) × π × r² = (60/360) × 3.14 × (6 cm)² = 18.84 cm².

What is the area of a sector of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14)

What is the area of a sector of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14)

Correct Answer: 18.84 cm²

Step 1: Identify the radius of the circle, which is given as 6 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 × r².
Step 4: Substitute the values into the formula: Area = (60/360) × 3.14 × (6 cm)².
Step 5: Calculate (6 cm)², which is 36 cm².
Step 6: Now substitute this value back into the formula: Area = (60/360) × 3.14 × 36 cm².
Step 7: Simplify (60/360) to 1/6.
Step 8: Now calculate Area = (1/6) × 3.14 × 36 cm².
Step 9: Multiply 3.14 by 36, which equals 113.04.
Step 10: Now divide 113.04 by 6 to find the area: 113.04 / 6 = 18.84 cm².

Area of a Sector – The area of a sector is calculated using the formula (θ/360) × π × r², where θ is the central angle in degrees and r is the radius.
Unit Consistency – Ensuring that all measurements are in the same units (e.g., cm) is crucial for accurate calculations.