What is the area of a sector of a circle with radius 10 cm and angle 90 degrees?

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Question: What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)

Options:

Correct Answer: 25π cm²

Exam Year: 2022

Solution:

Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².

What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)

What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)

Step 1: Identify the radius of the circle. In this case, the radius (r) is 10 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 × (10)².
Step 5: Calculate (10)², which is 100.
Step 6: Now the formula looks like this: Area = (90/360) × π × 100.
Step 7: Simplify (90/360) to (1/4).
Step 8: Now the formula is: Area = (1/4) × 100π.
Step 9: Calculate (1/4) × 100, which equals 25.
Step 10: Therefore, the area of the sector is 25π 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.