Question: A sector of a circle has a radius of 6 cm and a central angle of 60 degrees. What is the area of the sector?
Options:
12π cm²
6π cm²
3π cm²
9π cm²
Correct Answer: 6π cm²
Solution:
Area of sector = (θ/360) * πr² = (60/360) * π(6)² = (1/6) * 36π = 6π cm².
A sector of a circle has a radius of 6 cm and a central angle of 60 degrees. Wha
Practice Questions
Q1
A sector of a circle has a radius of 6 cm and a central angle of 60 degrees. What is the area of the sector?
12π cm²
6π cm²
3π cm²
9π cm²
Questions & Step-by-Step Solutions
A sector of a circle has a radius of 6 cm and a central angle of 60 degrees. What is the area of the sector?
Step 1: Identify the radius of the sector, which is given as 6 cm.
Step 2: Identify the central angle of the sector, which is given as 60 degrees.
Step 3: Use the formula for the area of a sector: Area = (θ/360) * πr².
Step 4: Substitute the values into the formula: Area = (60/360) * π * (6)².
Step 5: Calculate (6)², which is 36.
Step 6: Now the formula looks like this: Area = (60/360) * π * 36.
Step 7: Simplify (60/360) to (1/6).
Step 8: Now the formula is: Area = (1/6) * π * 36.
Step 9: Multiply (1/6) by 36 to get 6.
Step 10: Therefore, the area of the sector is 6π cm².
Area of a Sector – The area of a sector can be calculated using the formula (θ/360) * πr², where θ is the central angle in degrees and r is the radius.
Understanding Degrees – Recognizing that the central angle is given in degrees and how it relates to the full circle (360 degrees) is crucial for applying the formula correctly.
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