The height of the cylinder is 4 m, the distance between the axis of the cylinder and the parallel section plane is 3 m

The height of the cylinder is 4 m, the distance between the axis of the cylinder and the parallel section plane is 3 m, and the section area is 32 m2. Find the volume of a cylinder.

The section of the cylinder, parallel to its axis, is a rectangle, one side of which is the height of the cylinder, the other is the chord of the base. The area of ​​such a section is equal to the product of the height and the length of the chord. Therefore, the chord length can be found by dividing the sectional area by the cylinder height: l = 32/4 = 8 m.
The distance between the axis of the cylinder and the given section is a perpendicular drawn from the center of the base of the cylinder to the chord and dividing this chord in half.
Consider a right-angled triangle in which one leg is the distance from the axis of the cylinder to the chord, the second leg is half of the chord, and the base radius is the hypotenuse.
The sum of the squares of the legs is equal to the square of the hypotenuse, we can find the square of the radius of the base of the cylinder:
r ^ 2 = 3 ^ 2 + 4 ^ 2 = 9 + 16 = 25;
r = √25 = 5 m.
The volume of the cylinder is equal to the product of the height and the area of ​​the base: S = h * πr ^ 2 = 4 * π * 25 = 100π m3.