Question

The radius of a circle is 1. What is the length of an arc that subtends an angle of 10pi/9 radians?

Answer 1

3.5

Step-by-step explanation

We want to find the length of the arc that subtends 10pi/9 radians​.

To do that, we use the formula for length of an arc:

`\begin{gathered} S\text{ = }(\theta)/(2\pi)\cdot\text{ 2}\pi r \\ \text{where r = radius} \\ \theta\text{ = angle (in radians)} \end{gathered}`

Therefore, we have:

`\begin{gathered} S\text{ = }((10\pi)/(9))/(2\pi)\cdot\text{ 2 }\cdot\text{ }\pi\cdot\text{ 1} \\ S\text{ = }(10\pi)/(18\pi)\cdot\text{ 2 }\cdot\text{ }\pi\cdot\text{ 1} \\ S\text{ = 3.5} \end{gathered}`

That is the length of the arc.