Question

1. a sector of a circle has arc length 14 cm and central angle 2 radians. find its radius and area.

Explanation:

Step1: Recall arc - length formula

The arc - length formula is $l = r\theta$, where $l$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians. Given $l = 14$ cm and $\theta=2$ radians. We can solve for $r$ by rearranging the formula: $r=\frac{l}{\theta}$.
$r=\frac{14}{2}$

Step2: Calculate the radius

$r = 7$ cm

Step3: Recall the area formula for a sector

The area formula for a sector of a circle is $A=\frac{1}{2}r^{2}\theta$. We know $r = 7$ cm and $\theta = 2$ radians.
$A=\frac{1}{2}\times7^{2}\times2$

Step4: Calculate the area

$A=\frac{1}{2}\times49\times2=49$ $cm^{2}$

Answer:

Radius: 7 cm, Area: 49 $cm^{2}$