Question

In a circle , a 60 ° sector has area 25pi . What is the circumferenceof the circle ? Leave your answer in terms of and in simplest radical form .

Answer 1

`c=10\sqrt[]{6}\pi`

Explanation:

To calculate the area of the entire circle we must do it by means of a proportion, since the entire circle is 360 °, therefore

`(25\pi)/(60)=(x)/(360)`

Solving for x:

`\begin{gathered} x=(360\cdot25\pi)/(60) \\ x=150\pi \end{gathered}`

After calculating the area we can calculate the value of the radius, knowing that:

`\begin{gathered} A=\pi\cdot r^2 \\ \text{solving for r} \\ 150\pi=\pi\cdot r^2 \\ r=\sqrt[]{150} \\ r=5\sqrt[]{6} \end{gathered}`

Now, the formula for the circumference is the following:

`\begin{gathered} c=2\pi r \\ c=2\pi\cdot5\sqrt[]{6} \\ c=10\sqrt[]{6}\pi \end{gathered}`