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 =
`(\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* (\pi)/(4)`

`6=\pi r`

`(6)/(\pi)=r`

`(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.