The height of the cylinder is 2 cm, and the diagonal of the axial section makes

| June 21, 2021 | education

The height of the cylinder is 2 cm, and the diagonal of the axial section makes an angle of 30 ° with the base. Determine the volume of the cylinder.

The axial section of the cylinder is a rectangle passing through the axis of symmetry of the cylinder, the sides of which are the diameters of the circle at the base of the cylinder and its generatrices.

Then in a right-angled triangle ACB leg AB lies opposite an angle of 300, and then its length is equal to half the length of the hypotenuse, and therefore BC = 2 * AB = 2 * 2 = 4 cm.

Then, by the Pythagorean theorem, AC ^ 2 = BC ^ 2 – AB ^ 2 = 16 – 4 = 12.

AC = 2 * √3 cm, then AO = R = AC / 2 = 2 * √3 / 2 = √3 cm.

Determine the area of ​​the base of the cylinder. Sb = n * R2 = n * 3 cm2.

Determine the volume of the cylinder. V = Sosn * OO1 = n * 3 * 2 = 6 * n cm3.

Answer: The volume of the cylinder is 6 * n cm3.



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