Find the total surface area of the cylinder, if it is known that its height is 5 dm, and the diameter of the base is 10 dm.

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

Sp.p. = Sb.p. + 2 · Sosn;

The lateral surface area is equal to the product of Pi and twice the radius (diameter) of the base by the height:

Sb.p. = 2 * π * r * h = π * d * h;

Sb.p. = 3.14 * 10 * 5 = 157 cm2.

The base of a cylinder is a circle, so to calculate its area, we use the formula for the area of ​​a circle:

Sop = π * r ^ 2;

r = d / 2 = 10/2 = 5 cm;

Sb = 3.14 * 5 ^ 2 = 3.14 25 = 78.5 cm2.

Now the total surface area is:

Sp.p. = 157 + 2 * 78.5 = 157 + 157 = 314 cm2.

Answer: the total surface area of ​​the cylinder is 314 cm2.