Question: What is the area of a sector with a central angle of 90 degrees in a circle of radius 4 cm?
Options:
6.28 cm²
12.56 cm²
3.14 cm²
9.42 cm²
Correct Answer: 12.56 cm²
Solution:
Area of sector = (θ/360) * πr² = (90/360) * π(4)² = (1/4) * 16π = 4π ≈ 12.56 cm².
What is the area of a sector with a central angle of 90 degrees in a circle of r
Practice Questions
Q1
What is the area of a sector with a central angle of 90 degrees in a circle of radius 4 cm?
6.28 cm²
12.56 cm²
3.14 cm²
9.42 cm²
Questions & Step-by-Step Solutions
What is the area of a sector with a central angle of 90 degrees in a circle of radius 4 cm?
Area of a Sector – The area of a sector is calculated using the formula (θ/360) * πr², where θ is the central angle in degrees and r is the radius of the circle.
Understanding Central Angles – Recognizing that a 90-degree angle represents one-fourth of a full circle (360 degrees) is crucial for applying the sector area formula correctly.
Units of Measurement – Ensuring that the final area is expressed in square centimeters (cm²) is important for clarity and correctness.
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