Two planes are drawn through the generatrix of the cylinder; the angle between them is equal to 120

Two planes are drawn through the generatrix of the cylinder; the angle between them is equal to 120; the areas of the resulting sections are equal to 1; the radius of the base of the cylinder is equal to 1; find the volume of the cylinder

Since the planes of the sections are equal, and the height of the section is the generatrix of the cylinder, the chords A1B1 = A1C1 = AB = AC.

Let’s construct the radii of the circle OA1, OB1 and OC1.

The radius OA1 is the bisector of the angle B1A1C1, then the angle OA1C1 = 120/2 = 60.

The triangle ОА1С1 is equilateral since ОА1 = ОА1 = R = 1 unit, and the angle ОА1С1 = 60.

Then the chord A1C1 = 1 unit.

Let us determine the length of the generator AA1.

Saa1c1c = A1C1 * AA1 = 1 unit2.

AA1 = 1 unit.

The base area of the cylinder is equal to: Sb = π * R ^ 2 = π * 1 = π unit2.

Then V = Sosn * АА1 = π * 1 = π units3.

Since the planes of the sections are equal, and the height of the section is the generatrix of the cylinder, the chords A1B1 = A1C1 = AB = AC.

Let’s construct the radii of the circle OA1, OB1 and OC1.

The radius OA1 is the bisector of the angle B1A1C1, then the angle OA1C1 = 120/2 = 60.

The triangle ОА1С1 is equilateral since ОА1 = ОА1 = R = 1 unit, and the angle ОА1С1 = 60.

Then the chord A1C1 = 1 unit.

Let us determine the length of the generator AA1.

Saa1c1c = A1C1 * AA1 = 1 unit2.

AA1 = 1 unit.

The base area of the cylinder is equal to: Sb = π * R ^ 2 = π * 1 = π unit2.

Then V = Sosn * АА1 = π * 1 = π units3.