Question

In a circle with a radius of 4 centimeters, what is the length of an arc intercepted by a central angle of 2.5 radians?

Answer 1

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=4\\ \theta =2.5 \end{cases}\implies s=4(2.5)\implies s=10$

Answer 2

The length of an arc is the distance of the curved line, which has 2 endpoints and each of the endpoint is marked with the radius of the circle.

The length of the arc is 10 centimeters

The length (l) of an arc is:

$l =r\theta$

From the question, we have:

$r = 4$

$\theta = 2.5\ rad$

The length of the arc becomes:

$l =r\theta$

$l = 4 *2.5$

$l = 10$

Hence, the length of the arc is 10 centimeters

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