Question

Find the area swept by the door. Note: Enter your answer in terms of \piπpi.

Answer 1

We are asked to determine the area swept by the door. We notice that the area forms a sector of a circle. The area of the sector of a circle is given by:

`A=(1)/(2)r^2\theta`

Where:

`\begin{gathered} A=\text{ area} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}`

To convert the given angle into radians we use the following conversion factor:

`\pi\text{ radians = 180 degr}ees`

Now, we multiply by the conversion factor:

`45*(\pi)/(180)=(\pi)/(4)`

Now, we plug in the values in the formula for the area:

`A=(1)/(2)(80cm)^2((\pi)/(4))`

Solving the operations:

`A=800\pi cm^2`

Therefore, the area is 800 pi square centimeters.