Question

If this circle has a radius of 5.6 and mZc=120°, calculate the area of the intercepted sector (shaded blue). Round answers to two decimal places. Use the n button on your calculator.

Answer 1

ANSWER:

The area of the intercepted sector is square 32.82 units

STEP-BY-STEP EXPLANATION:

The first thing is to calculate the area of the whole circle, just like that

$A=\pi\cdot r^2$

replacing r = 5.6

$\begin{gathered} A=3.14\cdot5.6^2 \\ A=98.47 \end{gathered}$

Now, we multiply this area by the proportion of the desired sector, knowing that it has an angle of 120° and that of the circle is 360°

$\begin{gathered} A_S=98.47\cdot\frac{120\text{\degree}}{360\text{\degree}} \\ A_S=32.82 \end{gathered}$