Cylinder Calculator

Enter radius and height to calculate volume, surface area, and more.


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What is a Cylinder?

A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. Common examples include cans, pipes, and drums. A cylinder has a consistent circular cross-section throughout its height.

Cylinder Formulas

Volume Formula

The volume of a cylinder is the area of the base times the height:

V = Pi * r^2 * h

This can be thought of as stacking circular disks of area Pi*r^2 to height h.

Total Surface Area Formula

The total surface area includes both circular bases and the lateral (curved) surface:

A_total = 2 * Pi * r^2 + 2 * Pi * r * h
       = 2 * Pi * r * (r + h)

Lateral (Curved) Surface Area

The area of just the curved side:

A_lateral = 2 * Pi * r * h

This is equivalent to a rectangle with width = circumference (2*Pi*r) and height = h.

Base Area Formula

A_base = Pi * r^2

Components of a Cylinder

  • Radius (r): Distance from center to edge of the circular base
  • Height (h): Distance between the two bases
  • Diameter (d): Distance across the base = 2r
  • Base: The circular top and bottom
  • Lateral Surface: The curved side

Example Calculations

Example 1: Basic Cylinder

Given radius = 5 units and height = 10 units:

Volume = Pi * 5^2 * 10
      = Pi * 25 * 10
      = 250 * Pi
      = 785.4 cubic units

Lateral Area = 2 * Pi * 5 * 10
            = 100 * Pi
            = 314.16 square units

Total Surface Area = 2 * Pi * 5 * (5 + 10)
                  = 10 * Pi * 15
                  = 150 * Pi
                  = 471.24 square units

Example 2: Pipe Volume

A pipe has radius 2 cm and length 50 cm. What is its internal volume?

V = Pi * 2^2 * 50
V = Pi * 4 * 50
V = 200 * Pi
V = 628.32 cubic cm

Applications

Manufacturing

Designing cans, containers, pipes, and cylindrical tanks.

Engineering

Calculating material needed for pipes, hydraulic cylinders, and storage tanks.

Daily Life

Determining paint needed for cylindrical objects, water volume in tanks, or material for wrapping tubes.

Related Shapes

  • Cone: A cylinder tapering to a point
  • Prism: A cylinder with non-circular bases
  • Hollow Cylinder: A cylinder with a smaller cylinder removed (pipe)
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