Circle arc

Calculate the circular arc area in m² where the diameter is 263 dm and a central angle is 40°. Please result round to three decimal places.

Correct answer:

S =  60.361 m²

Step-by-step explanation:

$$\begin{gathered} d=263\text{dm} \\ r=d/2=263/2=\frac{263}{2}=131.5\text{dm} \\ k=\frac{40}{360}=\frac{1}{9}\doteq 0.1111 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 131.5^2\doteq 54325.2056{\text{dm}}^2 \\ {S}_2=k\cdot S_1=0.1111\cdot 54325.2056\doteq 6036.134{\text{dm}}^2 \\ S=S_2\to {\text{m}}^2=S_2:100{\text{m}}^2=6036.134:100{\text{m}}^2=60.361{\text{m}}^2=60.361{\text{m}}^2 \end{gathered}$$

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