The rectangle rotates around one of its sides, equal to 8cm. The lateral surface area of the cylinder obtained

The rectangle rotates around one of its sides, equal to 8cm. The lateral surface area of the cylinder obtained during rotation is 256pi cm2. Find the area of the rectangle.

Let the rectangle ABO1O rotate around the side OO1, then AB = СD = h = OO1 = 8 cm.

The AO segment is the radius of the circle and the unknown side of the rectangle. AO = R.

The lateral surface area of the cylinder is:

Side = 2 * π * R * AB = 2 * π * R * 8 = 16 * π * R = 256 * π cm2.

R = AO = 256 * π / 16 * π = 256/16 = 16 cm.

Then Savo1o = AO * AB = 16 * 8 = 128 cm2.

Answer: The area of the rectangle is 128 cm2.