Circle: Area, Circumference, Sector

For a circle of radius r, area is $A = \pi r^2$ and circumference is $C = 2\pi r$. For a sector of angle $\theta$ degrees, the area is $\frac{\theta}{360} \pi r^2$ and arc length is $\frac{\theta}{360} \cdot 2\pi r$.

Slide the radius r and the sector angle. The lab shows full area, circumference, sector area, and arc length together. Try r = 7, $\theta = 90$ degrees to see a quarter circle's sector area.

Students mix up $\pi r^2$ and $2\pi r$, using area where they need circumference. Remember: area has square units, circumference is in plain length units. Always check units before writing the final answer.

A cycle wheel of radius 35 cm travels $2\pi \times 35$ cm in one full turn, useful when computing distances. Pizza slices, fan blades and traffic roundabouts all use circle and sector ideas the lab covers.