The radius of the base of the cylinder is 4cm, the height is 5cm. Find the surface of the cylinder.

The lateral surface of the cylinder is equal to the product of twice the radius and the number π by the height:

Sb.p. = 2πrh;

Sb.p. = 2 * 3.14 * 4 * 5 = 125.6 cm2.

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

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

Since the base of the cylinder is a circle, its area is equal to:

Sosn. = πr ^ 2;

Sosn. = 3.14 * 4 ^ 2 = 3.14 * 16 = 50.24 cm2.

Now we can find the total surface area:

Sp.p. = 2 * 50.24 + 125.6 = 100.48 + 125.6 = 226.08 cm2.

Answer: the lateral surface area is 125.6 cm2, the total surface area is 226.08 cm2.