What is the area of a sector with a radius of 6 cm and a central angle of 120 de

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

Options:

Correct Answer: 12π cm²

Solution:

Area of sector = (θ/360) * πr² = (120/360) * π(6)² = (1/3) * 36π = 12π cm².

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

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

Step 1: Identify the formula for the area of a sector, which is Area = (θ/360) * πr².
Step 2: Plug in the values for θ (the central angle) and r (the radius). Here, θ = 120 degrees and r = 6 cm.
Step 3: Substitute the values into the formula: Area = (120/360) * π(6)².
Step 4: Simplify the fraction 120/360 to 1/3.
Step 5: Calculate (6)², which is 36.
Step 6: Multiply (1/3) by 36 to get 12.
Step 7: Finally, include π in the answer, so the area of the sector is 12π cm².

Area of a Sector – The area of a sector is calculated using the formula (θ/360) * πr², where θ is the central angle in degrees and r is the radius.
Unit Conversion – Understanding that the area is expressed in square centimeters (cm²) and ensuring the units are consistent.