A cylinder is formed by rotating a 5 cm diagonal rectangle around a 3 cm side. Find its total surface area.

Let us determine the length of the second side of the AВСD rectangle by the Pythagorean theorem.

AD ^ 2 = AC ^ 2 – СD ^ 2 = 25 – 9 = 16.

BP = 4 cm.

The AD side of the rectangle is the radii of the bases of the cylinder formed during rotation, and the СD side is its height.

Then Sop = π * AD ^ 2 = 16 * n cm2.

Side = π * AD * СD = π * 4 * 3 = 12 * n cm2.

Then Sпов = Sbok + 2 * Sсн = 12 * π + 2 * 16 * π = 48 * π cm2.

Answer: The surface area of rotation is 48 * π cm2.