Find the total surface area of the body of revolution: the side of the square is 8 cm.

The body of revolution of a square with a side of 8 cm is a cylinder, the height of which is 8 cm and the radius is also 8 cm (since all sides of the square are equal).

The total surface area of ​​a cylinder consists of the area of ​​its lateral surface and the area of ​​its two bases:

S.p. = Sb.p. + 2 · Sbn;

The lateral surface area of ​​a cylinder is equal to the product of the circumference of its base by its height:

Sb.p. = 2πrh;

The base area is calculated using the formula for the area of ​​a circle:

Sbn = πr ^ 2.

Thus, the total surface area of ​​the cylinder can be calculated as follows:

S.p. = 2πrh + 2πr ^ 2;

S.p. = 2 * 3.14 * 8 * 8 + 2 * 3.14 * 8 ^ 2 = 2 * 3.14 * 8 * 8 + 2 * 3.14 64 = 401.92 + 401.92 = 803, 84 cm2.

Answer: the total surface area of ​​the cylinder is 803.84 cm2.