Question

The circumference of Circle C is 1447.MAB1200СWhat is the length of AB?87167487967

Answer 1

The Solution.

First, we shall find the radius,r, of the given circle by using the formula below:

$\begin{gathered} C=2\pi r \\ C=144\pi,r=? \end{gathered}$

Substituting these values in the formula above, we get

$144\pi=2\pi r$

Dividing both sides by 2 pi, we get

$r=\frac{144\pi}{2\pi}=72$

Now, to find the length of arc AB, we shall use the formula below:

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

In this case,

$\theta=120,r=72,L=?$

Substituting these values in the formula above, we have

$\begin{gathered} L=\frac{120}{360}\times2\times\pi\times72 \\ \\ L=\frac{1}{3}\times2\times\pi\times72=2\times\pi\times24=48\pi \end{gathered}$

Hence, the correct answer is option 3.