Question

What is the area of a sector bounded by a 45 degree arc

Answer 1

To obtain the area of the sector, the following steps are necessary:

Step 1: Recall the general formula of the area of a sector, as follows

`A_(sector)=(\theta)/(360)*\pi* r^2`

Where:

`\begin{gathered} \theta=angle\text{ of the sector's arc} \\ r=\text{radius of the circle} \\ \pi=\text{ 3.142} \end{gathered}`

Step 2: Apply the formula to the question at hand, as follows:

`\begin{gathered} A_(sector)=(\theta)/(360)*\pi* r^2 \\ \text{where: }\theta=45^o,\text{ r= 10cm} \\ \text{Thus:} \\ A_(sector)=(45)/(360)*\pi*10^2 \\ \Rightarrow A_(sector)=(45)/(360)*\pi*100=(4500)/(360)*\pi \\ \Rightarrow A_(sector)=12.5*\pi=12.5\pi cm^2 \end{gathered}`

Therefore, in its simplest form, the area of the sector is 12.5π square centimeters