The radius of the base of the cylinder is 8 cm and the height is 2 times the circumference of the base.

The radius of the base of the cylinder is 8 cm and the height is 2 times the circumference of the base. Find the total surface area of the cylinder.

A cylinder is formed by rotating a rectangle around its side.

The total surface area of a cylinder is equal to the sum of the areas of its lateral surface and two bases:

Sp.p = Sb.p. + 2Ssn;

Since the height of the cylinder is twice the length of its base, then:

h = 4πr;

h = 4 * 8 * π = 32π.

Sb.p. = 2πrh;

Sb.p. = 2π * 8 * 32π = 512π ^ 2 = 5048.12 cm2;

Sosn. = πr ^ 2;

Sosn. = 8 ^ 2 * π = 64π = 200.96.

Sp.p = 5048.12 + 200.96 * 2 = 5048.12 + 401.92 = 5450.04 cm2.

Answer: the total surface area of the cylinder is 5450.04 cm2.