What you’ll learn
Calculate sector area.
Key idea
The whole circle area is pi times radius squared; scale it by the central-angle fraction.
Use squared radius and square units; boundary length is not area.
Worked example
Enter the exact value or ordered values in the format requested below.
A radius-3 cm circle has a 170-degree minor sector. Find exact sector area in square cm as a multiple of pi, without a unit suffix.
- Whole area=9π square cm; sector fraction=17/36.
- Sector area=17/36*9π=(17/4)π square cm.
Answer: (17/4)π
Quick Check
Evaluate a worked attempt at calculate sector area, identify the first invalid step, and provide the correction.
A radius-5 circle has a 100-degree sector. Step 1 finds fraction 100/360=5/18. Step 2 multiplies that by circumference 10π and calls (25/9)π the sector area. Locate and repair the first invalid step.