Irrigation sprinkler

The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate?

Correct result:

S =  402.1 m²

Solution:

$$\begin{gathered} A=320^{\circ } \\ r=12\text{ m } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 12^2\doteq 452.3893{\text{m}}^2 \\ S={\displaystyle \frac{A}{360}}\cdot S_1={\displaystyle \frac{320}{360}}\cdot 452.3893=402.1{\text{m}}^2 \end{gathered}$$

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