What is the area of a sector of a circle with a radius of 4 cm and a central ang

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Question: What is the area of a sector of a circle with a radius of 4 cm and a central angle of 90 degrees? (2014)

Options:

Correct Answer: 12.56 cm²

Solution:

Area of sector = (θ/360) * πr²; = (90/360) * π * 4² = 12.56 cm².

What is the area of a sector of a circle with a radius of 4 cm and a central angle of 90 degrees? (2014)

What is the area of a sector of a circle with a radius of 4 cm and a central angle of 90 degrees? (2014)

Step 1: Identify the radius of the circle. In this case, the radius (r) is 4 cm.
Step 2: Identify the central 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) * π * r².
Step 4: Substitute the values into the formula: Area = (90/360) * π * (4 cm)².
Step 5: Calculate (4 cm)², which is 16 cm².
Step 6: Now substitute this value back into the formula: Area = (90/360) * π * 16 cm².
Step 7: Simplify (90/360) to (1/4). So, Area = (1/4) * π * 16 cm².
Step 8: Multiply (1/4) by 16 cm², which gives 4 cm². So, Area = 4 cm² * π.
Step 9: Use the approximate value of π (3.14) to calculate the area: Area ≈ 4 cm² * 3.14 = 12.56 cm².

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