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

ANSWER:

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

STEP-BY-STEP 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

$\frac{25\pi}{60}=\frac{x}{360}$

Solving for x:

$\begin{gathered} x=\frac{360\cdot25\pi}{60} \\ x=150\pi \end{gathered}$

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:

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