Question

What is the area watered by the sprinkler? I can’t figure it out.

Answer 1

We are asked to determine the area of a circular sector. To do that we will use the following formula:

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

Where:

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

Now, we convert the angle of 85° to radians using the following conversion factor:

`1\pi=180\text{degrees}`

Now, we multiply by the conversion factor:

`\theta=85*(\pi)/(180)=(17\pi)/(36)`

Now, we substitute in the formula for the area:

`A=((5m)^2((17\pi)/(36))^2)/(2)`

Substituting the value of pi for 3.14

`A=((5m)^2((17(3.14))/(36))^2)/(2)`

Solving the operations:

`A=18.5m^2`

Therefore, the area is 18.5 square meters.