Find the total surface area and volume of a cylinder, the axial section of which is a square with a side of 6 cm.

Since the axial section ABCD is a square, the height of the cylinder is equal to the diameter of the circle at its base. AB = AD = 6 cm, then R = 6/2 = 3 cm.

Determine the area of the base of the cylinder.

Sbn = π * R ^ 2 = π * 9 cm2.

Determine the volume of the cylinder.

V = Ssc * AB = π * 9 * 6 = π * 54 cm3.

Let us determine the area of the lateral surface of the cylinder.

Side = 2 * π * R * AB = 2 * π * 3 * 6 = π * 36 cm2.

Then Sпов = 2 * Sсн + S side = 2 * π * 9 + π * 36 = π * 54 cm2.

Answer: The total surface area is π * 54 cm2, the volume is 54 * π cm3.