Question

Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.

Answer 1

Given:

Angle subtended at the center = 135 degrees

radius (r) = 4 yd

Solution

The formula for the length (l) of an arc is given as:

`\begin{gathered} l\text{ = }(\phi)/(360^0)\text{ }*\text{ 2}\pi r \\ \text{where }\phi\text{ is the angle subtend}ed\text{ at the center} \end{gathered}`

When we substitute the given parameters, we can find the length (l) of the arc:

`\begin{gathered} l\text{ = }(135)/(360)\text{ }*\text{ 2 }*\text{ }\pi\text{ }*\text{ 4} \\ =3\pi \\ \approx\text{ 9.4 yd (nearest tenth)} \end{gathered}`

Answer: 9.4 yd or 3.0 pi