The cone

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

Result

α =  60 °

Solution:

$S_1 = 2 = \pi r^2 \ \\ r = \sqrt{ 2/\pi} = 0.7979 \ cm \ \\ S_2 = 4 = \pi r s \ \\ s = 4/pi/r = 1.5958 \ cm \ \\ \cos \alpha = r/s \ \\ \alpha = \arccos r/s = 60 ^\circ$

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