# Segment CD, the ends of which lie on different circles of the cylinder bases, intersects the cylinder axis

Segment CD, the ends of which lie on different circles of the cylinder bases, intersects the cylinder axis at an angle of 60 degrees. Find the volume of the cylinder if CD is 8 cm long.

Triangle CO1K is rectangular, in which, according to the condition, the angle SKO1 = 600, then the angle KCO1 = (90 – 60) = 30. Then in the right-angled triangle CВD the leg of the ВD lies opposite the angle 300, then ВD = AD / 2 = 8/2 = 4 cm.
Then, in the ВСD triangle, according to the Pythagorean theorem, BC2 = СD2 – ВD2 = 64 – 16 = 48.
BC = 4 * √3 cm.
BO1 = R = BC / 2 = 4 * √3 / 2 = 2 * √3 cm.
Let’s define the volume of the cylinder.
V = π * R2 * ВD = π * 12 * 4 = 48 * π cm3.
Answer: The volume of the cylinder is 48 * π cm3.

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