Circle arc + section

Calculate the length of the arc of a circle and the volume of a circular section if the circle's radius is 8.3 centimeters and the central angle alpha=104 degrees.

Final Answer:

l =  15.0657 cm
S₂ =  62.5226 cm²

Step-by-step explanation:

$$\begin{gathered} r=8.3\text{cm} \\ \alpha =104{}^{\circ } \\ o=2\pi \cdot r=2\cdot 3.1416\cdot 8.3\doteq 52.1504\text{cm} \\ S=\pi \cdot r^2=3.1416\cdot 8.3^2\doteq 216.4243{\text{cm}}^2 \\ k=\frac{\alpha }{360}=\frac{104}{360}=\frac{13}{45}\doteq 0.2889 \\ l=k\cdot o=0.2889\cdot 52.1504=15.0657\text{cm} \end{gathered}$$

$S_2=k\cdot S=0.2889\cdot 216.4243=62.5226{\text{cm}}^2$

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