Question

Find the length of the indicated arc for the following circles. Either leave in terms of by entering answers with the word pi, or use 3.14 for pi and round your answer to the nearest 10th. If entering a fraction times pi, put pi in the numerator, for example enter as 2pi/3

Answer 1

We are given to find the length of the arc

Diameter = 12

Radius = 6

Angle = 110

Solution

The formula for finding the length of an arc (L) is given by

$L=\frac{\theta}{360}\times2\pi r$

Here

$\begin{gathered} r=6 \\ \theta=110^{\circ} \end{gathered}$

We now compute

$\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ L=\frac{110}{360}\times2\times\pi\times6 \\ L=\frac{11}{3}\times\pi \\ L=\frac{11\pi}{3} \end{gathered}$

We can also write the length in decimal

$\begin{gathered} L=\frac{11}{3}\times\pi \\ L=\frac{11}{3}\times3.14 \\ L=11.5133333 \\ L=11.5\text{ (to the nearest tenth)} \end{gathered}$