Question: What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
Options:
9π cm²
12π cm²
18π cm²
6π cm²
Correct Answer: 9π cm²
Exam Year: 2021
Solution:
Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².
What is the area of a sector of a circle with radius 6 cm and angle 90 degrees?
Practice Questions
Q1
What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
9π cm²
12π cm²
18π cm²
6π cm²
Questions & Step-by-Step Solutions
What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
Step 1: Identify the radius of the circle. Here, the radius (r) is 6 cm.
Step 2: Identify the 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: Area = (90/360) × π(6)².
Step 5: Simplify the fraction 90/360 to 1/4.
Step 6: Calculate (6)², which is 36.
Step 7: Multiply (1/4) by 36π: Area = (1/4) × 36π = 9π.
Step 8: Write the final answer: The area of the sector is 9π cm².
Area of a Sector – The area of a sector of a circle can be calculated using the formula (θ/360) × πr², where θ is the angle in degrees and r is the radius.
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