Question

A circle has a radius that is 4 centimeters long. if a central angle has a measure of 3 radians what is the length of the ark that corresponds in the angle?

Answer 1

12

Explanation:

Answer 2

There's a ratio that holds for arc lengths:


`\frac{\text{arc length}}{\text{measure of angle subtended by arc}}=\frac{\text{circumference}}{\text{one full revolution}}`

Denote the arc length by
`L` and the angle subtended by it by
`\theta`. Then given a circle of radius
`r`, this relation says


`\frac L\theta=(2\pi r)/(2\pi)=r\implies L=r\theta`

So, the arc length in this case is simply


`L=4\text{ cm}*3=12\text{ cm}`