Circular 4690

The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout?

Correct answer:

x =  133.7006 °

Step-by-step explanation:

$$\begin{gathered} r=20\text{cm} \\ h=50\text{cm} \\ s=\sqrt{r^2+h^2}=\sqrt{20^2+50^2}=10\sqrt{29}\text{cm}\doteq 53.8516\text{cm} \\ {S}_1=\pi \cdot r\cdot s \\ {S}_2=\pi \cdot s^2 \\ {x}_1=360\cdot S_1/S_2 \\ x=360\cdot \frac{r}{s}=360\cdot \frac{20}{53.8516}=133.7006^{\circ }=133°42^{\prime }2" \end{gathered}$$

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