Angle of the sector

Find the angle of the sector of a circle radius of 20 units where the area is equal to the lateral area of a cone with a radius of 8 units.

Final Answer:

α =  81.4587 °

Step-by-step explanation:

$$\begin{gathered} r_1=20 \\ {r}_2=8 \\ {h}_2=r_2=8 \\ s=\sqrt{h_2^2+r_2^2}=\sqrt{8^2+8^2}=8\sqrt{2}\doteq 11.3137 \\ A=\pi \cdot r_2\cdot s=3.1416\cdot 8\cdot 11.3137\doteq 284.3445 \\ A=\pi \cdot r_1^2\cdot \alpha /360 \\ \alpha =\frac{360\cdot A}{\pi \cdot r_1^2}=\frac{360\cdot 284.3445}{3.1416\cdot 20^2}=81.4587^{\circ }=81°27^{\prime }31" \end{gathered}$$

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