Find the area of the axial section of the cylinder if its diameter is 8 cm and the diagonal of the axial section is 10 cm.

1. By the condition of the problem, it is known that the diameter of the cylinder is 8 cm, and the diagonal of the axial section is 10 cm.

2. The required area S of the axial section, which is a rectangle, will be calculated as the product of its width and length.

The width is the height h of the cylinder, the value of which is determined from a right-angled triangle with a leg of 8 cm and a hypotenuse of 10 cm according to the Pythagorean theorem:

h = √10² – 8² = √100 – 64 = √36 = 6 cm.

S = 8 cm * 6 cm = 48 cm².

Answer: The axial cross-sectional area of the cylinder is 48 cm².