The diagonal of the main section of the cylinder = 8 cm and is inclined to the plane of the base of the cylinder

The diagonal of the main section of the cylinder = 8 cm and is inclined to the plane of the base of the cylinder at an angle of 30 degrees. Find the volume of the cylinder.

Since the diagonal of the section is inclined to the base plane at an angle of 30 °, the height of the cylinder h is:

8 * sin (30 °) = 8 * 1/2 = 4.

The side of the section belonging to the base plane is equal to:

8 * cos (30 °) = 8 * √3 / 2 = 4√3.

Then the radius of the cylinder is R:

4√3: 2 = 2√3.

We find the volume of the cylinder by the formula:

V = π * R ^ 2 * h.

V = π * (2√3) ^ 2 * 4 = 48.

Answer: the required cylinder volume is 48.