Point O is the middle of the cylinder axis. The generatrix of the cylinder is visible from point O at an angle

| August 19, 2021 | education

Point O is the middle of the cylinder axis. The generatrix of the cylinder is visible from point O at an angle, the degree measure of which is 60 degrees, and the distance from point O to the point of the circumference of the base of the cylinder is 4 cm. Calculate the volume of the cylinder.

Since point O is the middle of the O1O2 axis, then O1O2 = 2 * OO1 = 2 * 4 = 8 cm.

Then the height AB = О1О2 = h = 8 cm.

Rectangular triangles OO2B and OO1A are equal in two legs, then OA = OB.

The generatrix AB is seen from point O at an angle of 600, then the triangle AOB is equilateral, OA = OB = AB = 8 cm.

In a right-angled triangle OAO1, the angle OAO1 = 90 – 60 = 300.

Then AO1 ^ 2 = R ^ 2 = AO ^ 2 – OO1 ^ 2 = 64 – 16 = 48.

AO1 = R = 4 * √3 cm.

Determine the volume of the cylinder.

V = π * R ^ 2 * h = π * 48 * 8 = π * 384 cm3.

Answer: The volume of the cylinder is π * 384 cm3.



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