Right Cylinder Calculator

Calculate volume, lateral surface area, and total surface area of a right cylinder with step-by-step solutions.

Enter Cylinder Dimensions

Result

Volume
--
cubic units
Lateral (Side) Surface Area --
Base Area (one circle) --
Total Surface Area --
Diameter --
Base Circumference --

Step-by-Step Solution

V = pi x r^2 x h

What is a Right Cylinder?

A right cylinder is a three-dimensional geometric solid with two parallel circular bases connected by a curved surface. The term "right" means that the axis connecting the centers of the two bases is perpendicular to both bases. It is one of the most common 3D shapes encountered in daily life and engineering.

Cylinder Formulas

Volume

The base area times the height gives the total volume.

V = pi x r² x h

Lateral Surface Area

The curved surface area when the cylinder is "unrolled" into a rectangle.

LA = 2 x pi x r x h

Total Surface Area

The lateral area plus the area of both circular bases.

SA = 2 x pi x r x (r + h)

Understanding the Lateral Surface

If you cut a cylinder's lateral surface along a vertical line and unroll it, you get a rectangle. The width of this rectangle equals the circumference of the base (2 x pi x r), and the height equals the cylinder's height (h). Therefore, the lateral area = 2 x pi x r x h.

Real-World Applications

  • Cans and containers: calculating capacity and material needed for manufacturing.
  • Pipes and tubes: determining flow capacity and surface area for insulation.
  • Silos and tanks: agricultural and industrial storage calculations.
  • Columns in architecture: computing volume of material and surface to paint.
  • Engine cylinders: calculating displacement volume in automotive engineering.

Cylinder vs. Cone vs. Sphere

For the same radius and height, a cone has one-third the volume of a cylinder. A sphere with the same radius has a volume of (4/3) x pi x r³. These relationships are fundamental in comparing 3D shapes and were first rigorously proven by Archimedes.