The cone

The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane.
(The cone side is the segment joining the vertex cone with any point of the base circle. All sides of the cone form the shell of the cone.)

Correct answer:

α =  60 °

Step-by-step explanation:

$$\begin{gathered} S_1=2=\pi r^2 \\ r=\sqrt{2/\pi }=0.7979cm \\ {S}_2=4=\pi rs \\ s=4/pi/r=1.5958cm \\ \cos \alpha =r/s \\ \alpha =\arccos r/s=60^{\circ } \end{gathered}$$

Try another example