A sector of a circle has a radius of 5 cm and a central angle of 60 degrees. Wha
Practice Questions
Q1
A sector of a circle has a radius of 5 cm and a central angle of 60 degrees. What is the area of the sector?
13.09 cm²
25 cm²
15.71 cm²
20.94 cm²
Questions & Step-by-Step Solutions
A sector of a circle has a radius of 5 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 5 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 * (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 can be calculated using the formula (θ/360) * πr², where θ is the central angle in degrees and r is the radius of the circle.
