What is the area of a sector of a circle with a radius of 6 cm and a central ang

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Question: What is the area of a sector of a circle with a radius of 6 cm and a central angle of 120 degrees?

Options:

Correct Answer: 24π cm²

Solution:

Area of sector = (θ/360) * πr² = (120/360) * π(6)² = 12π cm².

What is the area of a sector of a circle with a radius of 6 cm and a central angle of 120 degrees?

What is the area of a sector of a circle with a radius of 6 cm and a central angle of 120 degrees?

Step 1: Identify the radius of the circle. In this case, the radius (r) is 6 cm.
Step 2: Identify the central angle of the sector. Here, the angle (θ) is 120 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 = (120/360) * π * (6)².
Step 5: Calculate (6)², which is 36.
Step 6: Now the formula looks like this: Area = (120/360) * π * 36.
Step 7: Simplify (120/360) to (1/3).
Step 8: Now the formula is: Area = (1/3) * π * 36.
Step 9: Multiply (1/3) by 36, which gives you 12.
Step 10: So, the area of the sector is 12π 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 central angle in degrees and r is the radius.
Circle Geometry – Understanding the properties of circles, including radius, diameter, and the relationship between angles and arc lengths.