walec

Walec is the Polish term for the solid known in English as a cylinder. It is a three-dimensional shape formed by two parallel, congruent circular bases and a curved lateral surface connecting corresponding points on the bases. The bases lie in two parallel planes, and the distance between these planes is the height h. The radius of each base is r, and the axis is the line through the centers of the bases. If the axis is perpendicular to the bases, the walec is a right circular walec; if the axis is tilted, the figure is an oblique walec.

In a right circular walec, the volume is V = π r^2 h. The lateral surface area is L = 2π r h, and the total surface area is A = 2π r h + 2π r^2 = 2π r (h + r). A plane parallel to the bases intersects the walec in a rectangle of dimensions h by 2r, while a plane containing the axis also yields a rectangle of the same dimensions.

Walec shapes appear in many applications, including cylinders and tanks, pipes and tubes, rolling components, and various containers. They are fundamental in geometry, engineering, and design due to their simple yet versatile surface and volume properties.