Question

Find the radius of a circle given that a central angle of measure pi/4 intercepts an arc of length 1.5in

Answer 1

Given:

Central angle = $\dfrac{\pi}{4}$

Arc length = 1.5 in

To find:

The radius of the circle.

Solution:

We know that the formula for arc length is

$s=r\theta$

Where r is radius and $\theta$ is the central angle in radian.

Substitute the given values in the above formula.

$1.5=r\times \dfrac{\pi}{4}$

$6=\pi r$

$\dfrac{6}{\pi}=r$

$\dfrac{6}{3.14}=r$

On further simplifiation, we get

$r=1.910828$

$r\approx 1.91$

Therefore, the radius of the circle is 1.91 in.