How Do I Calculate the Volume of a Tube?

By Allan Robinson
Cylinder with radius r and height h

Let a tube be any solid that has cross-sections of equal area throughout its length. However, a tube is generally a cylinder unless otherwise specified. Basic geometry defines a cylinder as the surface formed by the set of points that are a fixed distance from a given line segment (axis of the cylinder). You can calculate the volume area of a cylinder if you know its radius and height. You may also calculate the volume of any tube from its height and cross-sectional area.

Identify the parts of a cylinder. The radius r of a cylinder is the radius of the circle that forms its base. Note that any cross-section of the cylinder that is perpendicular to the base of the cylinder is a circle of the radius. The height h of a cylinder is the length of the cylinder's axis.

Determine the area A of the cylinder's base. The area of the base is (pi)(r^2) since the base is a circle of radius r.

Calculate the volume of the cylinder. The volume of any tube is V = hA, where V is the volume, h is its height and A is the area of a cross-section. Therefore, we have V = Ah = (pi)(r^2)h.

Find the volume of a specific cylinder. The volume of a cylinder with radius 3 and height 4 is V = (pi)(r^2)h = (pi)(3^2)(4) = (pi)(9)(4) = 36 (pi).

Identify solids for which V = Ah. We can use integral calculus to show that this formula for volume will work for any solid with a known height h and known base area if all cross-sections that are perpendicular to the base along the height h have the same area. Note that the cross-sections do not need to have the same shape.


About the Author

Allan Robinson has written numerous articles for various health and fitness sites. Robinson also has 15 years of experience as a software engineer and has extensive accreditation in software engineering. He holds a bachelor's degree with majors in biology and mathematics.