What is the area of a sector of a circle with a radius of 7 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 7 cm and an angle of 90 degrees? (2022)

Options:

Correct Answer: 38.5 cm²

Exam Year: 2022

Solution:

Area of sector = (θ/360) * πr² = (90/360) * π * 7² = 38.5 cm².

What is the area of a sector of a circle with a radius of 7 cm and an angle of 90 degrees? (2022)

What is the area of a sector of a circle with a radius of 7 cm and an angle of 90 degrees? (2022)

Step 1: Identify the radius of the circle, which is given as 7 cm.
Step 2: Identify the angle of the sector, which is given as 90 degrees.
Step 3: Recall 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 * (7 cm)².
Step 5: Calculate (7 cm)², which is 49 cm².
Step 6: Now substitute this value back into the formula: Area = (90/360) * π * 49 cm².
Step 7: Simplify (90/360) to (1/4).
Step 8: Now calculate the area: Area = (1/4) * π * 49 cm².
Step 9: Multiply (1/4) by 49 cm² to get 12.25 cm², then multiply by π (approximately 3.14).
Step 10: The final area is approximately 38.5 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.