cilinders

Cilinders are geometric figures defined as solid or hollow shapes with two parallel bases that are congruent circles and a curved side surface joining them. If the bases are perpendicular to the axis, the figure is a right circular cylinder; if the axis is inclined relative to the bases, it is an oblique cylinder. Cylinders can be solid or hollow, as in pipes or tubes.

For a right circular cylinder with base radius r and height h, the volume is V = π r^2 h, and the surface area of a solid cylinder is A = 2π r (r + h). The lateral surface area is 2π r h, and the two bases contribute 2π r^2. For a hollow cylinder with outer radius Ro, inner radius Ri, and height h, the volume is V = π h (Ro^2 − Ri^2), the lateral area is 2π h (Ro + Ri), and the total surface area is A = 2π h (Ro + Ri) + 2π (Ro^2 − Ri^2).

In engineering and industry, cylinders serve both as geometric models and as functional components. Piston cylinders are used in internal combustion engines and hydraulic or pneumatic actuators. Cylindrical tanks, pipes, rollers, and structural members rely on cylindrical forms for strength and manufacturability.

Materials and production methods vary by application. Common materials include steel and aluminum alloys, plastics, and composites. Manufacturing techniques include extrusion, casting, drilling and turning, and final machining to achieve precise tolerances.