Question

a central angle $\theta$ is drawn in a circle of radius $r$. (a) the length of the arc subtended by $\theta$ is $s = square$. (b) the area of the sector with central angle $\theta$ is $a=square$.

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc \(s\) of a circle with radius \(r\) and central - angle \(\theta\) (in radians) is \(s = r\theta\).

Step2: Recall sector - area formula

The formula for the area \(A\) of a sector of a circle with radius \(r\) and central - angle \(\theta\) (in radians) is \(A=\frac{1}{2}r^{2}\theta\).

Answer:

(a) \(s = r\theta\)
(b) \(A=\frac{1}{2}r^{2}\theta\)