Question

A circle has a radius of 2 feet. What is the area of a sector when the central angle is 15 degrees?

Answer 1

Hello!

First, let's calculate the area of the whole circle, using the formula:

$\begin{gathered} A_{\circ}=\pi\cdot r^2 \\ A_{\circ}=3.14\cdot2^2 \\ A_{\operatorname{\circ}}=3.14\times4 \\ A_{\operatorname{\circ}}=12.56 \end{gathered}$

Now, remember: the central angle is 15º, and we calculated considering 360º (whole circle). So, let's divide it, look:

$\frac{360\degree}{15\degree}=24$

In 360º, there are 24 sectors with 15º each. So, let's divide the obtained area by 24 to obtain the area of one sector:

$\frac{12.56}{24}\cong0.52\text{ feet}^2$