Question

The radius of a circle is 1 kilometer. What is the area of a sector bounded by a 45 degree arc?Give the exact answer in simplest form._____ square kilometers.

Answer 1

We can find the area of the sector of a circle with the following equation:

$A=\frac{N}{360}(\pi r^2)$

Where N is the angle that defines the sector of the circle. In this case, we have the following:

$\begin{gathered} N=45\degree \\ r=1\operatorname{km} \end{gathered}$

then, using the formula for the area of the sector, we get:

$\begin{gathered} A=\frac{45}{360}\pi\cdot(1)^2=\frac{1}{8}\pi \\ \Rightarrow A=\frac{1}{8}\pi \end{gathered}$

therefore, the area of the sector bounded is 1/8 pi