What is the area of a sector of a circle with a radius of 4 cm and an angle of 9

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Question: What is the area of a sector of a circle with a radius of 4 cm and an angle of 90 degrees? (2023)

Options:

Correct Answer: 2π cm²

Exam Year: 2023

Solution:

Area of sector = (θ/360) × πr²; = (90/360) × π(4)² = 2π cm².

What is the area of a sector of a circle with a radius of 4 cm and an angle of 90 degrees? (2023)

What is the area of a sector of a circle with a radius of 4 cm and an angle of 90 degrees? (2023)

Step 1: Identify the formula for the area of a sector of a circle, which is Area = (θ/360) × πr².
Step 2: Substitute the values into the formula. Here, θ (the angle) is 90 degrees and r (the radius) is 4 cm.
Step 3: Calculate the area by plugging in the values: Area = (90/360) × π(4)².
Step 4: Simplify the fraction 90/360 to get 1/4.
Step 5: Calculate (4)², which is 16.
Step 6: Now multiply: Area = (1/4) × π × 16.
Step 7: Simplify the multiplication: Area = 4π cm².
Step 8: Therefore, the area of the sector is 4π cm².

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