A circles has radius 10 centimeters. Suppose an arc on the circle has length 8\pi centimeters. what is the measure of the central angle whose radii define the arc?

Question

A circles has radius 10 centimeters. Suppose an arc on the circle has length 8
`\pi` centimeters. what is the measure of the central angle whose radii define the arc?

Answer 1

The measure of the central angle whose radii define the arc is
`\mathbf{(4\pi )/(5) }`

Explanation:

Radius of circle = 10 cm

Length of arc =
`8\pi`

We need to find Theta
`\theta`

The formula used will be:
`S=r \theta`

S= length of arc, r = radius and
`\theta` = angle

Putting values and finding \theta

`S=r \theta\\8\pi =10 \theta\\\theta=(8\pi )/(10) \\\theta=(4\pi )/(5)`

So, the measure of the central angle whose radii define the arc is
`\mathbf{(4\pi )/(5) }`