The radius of the axis of the cylinder-2m height-3m find: the diagonal of the axial section

The radius of the axis of the cylinder-2m height-3m find: the diagonal of the axial section, base area, side area, total area, volume of the cylinder.

Since the cylinder is formed by the rotation of a rectangle, then its axial section is also a rectangle. For convenience, we will designate it as ABCD. AB, in this case, is the height, BC is the base diameter, AC is the diagonal of the axial section. Let’s apply the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = (2 + 2) ^ 2 + 3 ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25;

AC = √25 = 5 m.

The base of the cylinder is a circle, therefore, to calculate its area, we apply the formula:

Sosn. = πr ^ 2;

Sosn. = 3.14 * 2 ^ 2 = 3.14 * 4 = 12.56 m2.

The lateral surface area of ​​the cylinder is calculated by the formula:

Sb.p. = 2πrl;

Sb.p. = 2 * 3.14 * 2 * 3 = 37.68 m2.

The total surface area is equal to the sum of the areas of the base and the lateral surface:

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

Sp.p. = 2 * 12.56 + 37.68 = 25.12 + 37.68 = 62.8 m2.

The volume of a cylinder is equal to the product of the base area by the height:

V = Sb. * h = πr2h;

V = 12.56 * 3 = 37.68 m3.

Answer: АС = 5m, Sosn. = 12.56 m2, Sb.p. = 37.68 m2, Sp.p. = 62.8 m2, V = 37.68 m3.