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:

$A=\frac{r^2\theta}{2}$

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:

$\theta=85\times\frac{\pi}{180}=\frac{17\pi}{36}$

Now, we substitute in the formula for the area:

$A=\frac{(5m)^2(\frac{17\pi}{36})^2}{2}$

Substituting the value of pi for 3.14

$A=\frac{(5m)^2(\frac{17(3.14)}{36})^2}{2}$

Solving the operations:

$A=18.5m^2$

Therefore, the area is 18.5 square meters.