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=(144\pi)/(2\pi)=72`

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

`L=(\theta)/(360)*2\pi r`

In this case,

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

Substituting these values in the formula above, we have

`\begin{gathered} L=(120)/(360)*2*\pi*72 \\ \\ L=(1)/(3)*2*\pi*72=2*\pi*24=48\pi \end{gathered}`

Hence, the correct answer is option 3.