Question

INFORMATION: The security camera (placed where the label CAM is in the bottom left corner) is advertised to cover a 90° sector with a radius of 30 yds. YOUR TASK: What area is safely monitored by the security camera? Camera Area of full circle: 90° Sector Area

Answer 1

we know that

The area of a circle is

`A=\pi\cdot r^2`

we have

r=30 yd

substitute

`\begin{gathered} A=\pi\cdot(30)^2 \\ A=900\pi\text{ yd\textasciicircum{}2} \end{gathered}`

The area of full circle is 900pi square yards

Find out the area of 90 degrees sector

Remember that

The area of a 90 degrees sector is one fourth of the area of the full circle

so

`\begin{gathered} A=((1)/(4))\cdot900\pi \\ A=225\pi\text{ yd\textasciicircum{}2} \\ \end{gathered}`

therefore

the area of a 90 degrees sector is 225pi square yards