Question

On a circle of a radius $r$,a central angle of $\theta$radians subtends an arc of length $s=\_\_\_\_\_\_\_\_$; the area of the sector formed by this angle $\theta$is $A=\_\_\_\_\_\_\_\_$.

Short answer

The solution is$s=r·\theta$,$A=\left(\frac{\theta }{360°}\right)\times {\mathrm{\pi r}}^2$.

Step-by-step solution

Step 1. Given information 

The radius $r$a circle and a central angle of $\theta$radians

Step 2. Calculation  

On a circle of a radius $r$,a central angle of $\theta$radians subtends an arc of length $s=r·\theta$; the area of the sector formed by this angle is $A=\left(\frac{\theta }{360°}\right)\times {\mathrm{\pi r}}^2$.