The diameter of the base of the cylinder is 10, and its generatrix is 15.

The diameter of the base of the cylinder is 10, and its generatrix is 15. The section parallel to the axis of the cylinder is at a distance equal to 4. Find the area of this section.

Consider a right-angled triangle ОНB, in which the angle В = 90, the hypotenuse ОВ is equal to half the diameter of the base, ОВ = BК / 2 = 10/2 = 5 cm, the leg ОН is the distance from the section to the center of the circle.

Then the HB leg is defined by the Pythagorean theorem. HB ^ 2 = OB ^ 2 – OH ^ 2 = 25 – 16 = 9.

HB = 3 cm.

Then BC = 2 * BH since the BC chord is divided in half by the radius of the circle. BC = 2 * 3 = 6 cm.

Then the cross-sectional area is equal to:

Savsd = 6 * 15 = 90 cm2.

Answer: The cross-sectional area is 90 cm2.