The main section of a cylinder is a square with a diagonal of 6√2 cm. Find the volume of a cylinder?

Since the axial section is square, the diagonal AC divides the section into yes rectangular isosceles triangles. AB = AD.

Then AC ^ 2 = 2 * AB ^ 2 = 2 * AD ^ 2.

AB = AD = √AC2 / 2 = √36 = 6 cm.

Since the section is axial, AD is the diameter of the circle at the base of the cylinder.

Then R = АD / 2 = 6/2 = 3 cm.

Determine the area of the base of the cylinder. Sb = π * R2 = 9 * π cm2.

Then V = Sosn * AB = 9 * π * 6 = 54 * π cm3.

Answer: The volume of the cylinder is 54 * π cm3.