Question: If a circle has a radius of 5 cm, what is the area of the sector formed by a 60-degree angle?
Options:
13.09 cm²
25.00 cm²
15.71 cm²
20.94 cm²
Correct Answer: 13.09 cm²
Solution:
Area of sector = (θ/360) * πr² = (60/360) * π(5)² = (1/6) * 25π ≈ 13.09 cm².
If a circle has a radius of 5 cm, what is the area of the sector formed by a 60-
Practice Questions
Q1
If a circle has a radius of 5 cm, what is the area of the sector formed by a 60-degree angle?
13.09 cm²
25.00 cm²
15.71 cm²
20.94 cm²
Questions & Step-by-Step Solutions
If a circle has a radius of 5 cm, what is the area of the sector formed by a 60-degree angle?
Step 1: Identify the radius of the circle, which is given as 5 cm.
Step 2: Identify the 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 * (5)².
Step 5: Calculate (5)², which is 25.
Step 6: Now the formula looks like this: Area = (60/360) * π * 25.
Step 7: Simplify (60/360) to (1/6).
Step 8: Now the formula is: Area = (1/6) * 25π.
Step 9: Calculate (1/6) * 25, which is approximately 4.17.
Step 10: Multiply 4.17 by π to get the area, which is approximately 13.09 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.
Understanding Degrees – Recognizing that the angle must be in degrees for the formula to apply correctly.
Substituting Values – Correctly substituting the values of θ and r into the formula to find the area.
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