The diagonal of the axial section of the cylinder is 10 cm. Find the area of this section if the height of the cylinder is 6 cm.

Since the cylinder is formed by rotating a rectangle around its side, the axial section of this cylinder will also be a rectangle. Let’s designate it AВСD. The diagonal of this section AC is 10 cm and the height AB is 6 cm.

In order to find the area of ​​the axial section of the AВСD, it is necessary to find the diameter of the base of the cylinder ВС. To do this, consider the triangle ABC, formed by the diagonal of the axial section. Let’s apply the Pythagorean theorem:

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

BC ^ 2 = AC ^ 2 – AB ^ 2;

BC ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

BC = √64 = 8 cm.

The area of ​​a rectangle is equal to the product of length and width:

S = AB * BC;

S = 6 * 8 = 48 cm2.

Answer: the cross-sectional area is 48 cm2.