Circle arc

The circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and the size of the central angle.

Correct answer:

r =  31.0007 dm
f =  250 °

Step-by-step explanation:

$$\begin{gathered} a\cdot r=135.26 \\ {r}^2\cdot a/2=2096.58 \\ {r}^2\cdot (135.26/r)/2=2096.58 \\ 135.26r=4193.16 \\ r=\frac{4193.16}{135.26}=31.00073932 \\ r=31.000739 \\ a=135.26/r=135.26/31.0007\doteq 4.3631\text{rad} \\ r=31.0007=31.0007\text{dm} \end{gathered}$$

$f=a\to \text{°}=a\cdot \frac{180}{\pi }\text{°}=4.3631\cdot \frac{180}{\pi }\text{°}=250\text{°}=250^{\circ }=249°59^{\prime }18"$

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