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=(N)/(360)(\pi r^2)`

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

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

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

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