Hollow Cylinder Volume Calculator

Calculate the volume, wall thickness, and cross-section area of a hollow cylinder (pipe or tube) with step-by-step solutions.

Enter Dimensions

Result

Hollow Cylinder Volume
2402.610738
cubic units
Outer Radius (R) 10 units
Inner Radius (r) 7 units
Height (h) 15 units
Wall Thickness 3 units
Cross-Section Area 160.174049 sq units
Outer Volume (solid) 4712.38898 cubic units
Inner Volume (hollow) 2309.778242 cubic units
Outer Surface Area 942.477796 sq units
Inner Surface Area 659.734457 sq units
Total Surface Area 1922.560352 sq units

Step-by-Step Solution

V = pi x h x (R^2 - r^2)

What Is a Hollow Cylinder?

A hollow cylinder (also called a cylindrical shell, tube, or pipe) is a three-dimensional shape formed by two coaxial cylinders. It has an outer radius R and an inner radius r, with the material filling the space between them. Common examples include pipes, tubes, drinking straws, rings, and bushings.

Hollow Cylinder Formulas

Volume

The volume of material in the hollow cylinder.

V = pi x h x (R2 - r2)

Cross-Section Area

The annular (ring) area of the cross-section.

A = pi x (R2 - r2)

Wall Thickness

The thickness of the wall material.

t = R - r

Total Surface Area

Outer + inner lateral surfaces + two annular ends.

SA = 2pi(R+r)h + 2pi(R2-r2)

Outer Lateral Area

The outer curved surface area.

Aouter = 2 x pi x R x h

Inner Lateral Area

The inner curved surface area.

Ainner = 2 x pi x r x h

Understanding the Volume Formula

The volume of a hollow cylinder can be understood as the difference between the volume of the outer solid cylinder and the inner hollow space:

V = V_outer - V_inner = pi x R^2 x h - pi x r^2 x h = pi x h x (R^2 - r^2)

This can also be factored as: V = pi x h x (R + r)(R - r), which shows that the volume depends on both the average radius and the wall thickness.

Practical Applications

  • Plumbing: Calculating the volume of pipe material for weight and cost estimation
  • Engineering: Determining material volumes for cylindrical bushings, bearings, and sleeves
  • Manufacturing: Computing the volume of hollow tubes for extrusion and casting processes
  • Fluid dynamics: Calculating the volume of fluid that can fill a pipe (inner volume)
  • Construction: Estimating concrete needed for cylindrical columns with hollow cores

Step-by-Step Example

Find the volume of a hollow cylinder with outer radius R = 10, inner radius r = 7, and height h = 15:

  1. Calculate R^2 - r^2 = 100 - 49 = 51
  2. Multiply by pi: pi x 51 = 160.2212
  3. Multiply by height: V = 160.2212 x 15 = 2403.318
  4. Wall thickness: t = 10 - 7 = 3