# Hollow cylinder volume, area, surface area and circumference

This calculator will calculate the various properties of a tube, also called a pipe or hollow cylinder for given values for inner-outer radius and height. The hollow circular cylinder is a three-dimensional solid confined by two parallel cylindrical surfaces having two parallel circular bases. The shortest distance from the center of the circular base to the inner cylinder is called as inner radius, and the shortest distance from the center of the circular base to the outer cylinder is called outer radius.

__The formulas and Definitions:__**Area of a Hollow Cylinder:**

2π ( r_{1} + r_{2})( r_{1} – r_{2} +h)

**outer radius**of the given cylinder, \(\mathbf{r_{2}}\) is

**inner radius**and \(\mathbf{h}\) is

**height**. \(\mathbf{C_{1}}\) is the outer circumference and \(\mathbf{C_{2}}\) is the inner circumference. L

_{1}and L

_{2}is the outer and inner surface areas respectively. t be the thickness of the cylinder (\(\mathbf{r_{1}- r_{2}}\))

**Area of Hollow Cylinder formulas:**

The Circumference of a circle (C) is given by:

\(C = 2\pi r\), therefore,\(C_{1} = 2\pi r_{1}\) \(C_{2} = 2\pi r_{2}\)

The Lateral Surface Area (L),for a cylinder is:\(L = C \times h = 2 \pi r h\), therefore,

\(L_{1} = 2 \pi r_{1} h\), the external curved surface area

\(L_{2} = 2 \pi r_{2} h\), the internal curved surface area

**Lateral Surface Area of a hollow cylinder**= \(L = 2 \pi r_{1} h + 2 \pi r_{2} h\)

The Cross sectional Area:

Let A is the area of a cross-section of a hollow cylinder, \(\pi r^{2}\), for a circle, therefore;

A

_{1}= \(\pi r_{1}^{2}\) for the area enclosed by \(r_{1}\)

A

_{2}= \(\pi r_{2}^{2}\)for the area enclosed by \(r_{2}\)

A = A

_{1}– A

_{2}for the cross sectional area of hollow cylinder

A = \(\pi r_{1}^{2}- \pi r_{2}^{2} = \pi (r_{1}^{2}- r_{2}^{2})\)

Total Surface Area of a Hollow Cylinder:

=\(2 \pi h (r_{1}+ r_{2}) + 2 \pi (r_{1}^{2} – r_{2}^{2})\)

=\(2 \pi h (r_{1}+ r_{2}) + 2 \pi (r_{1} + r_{2}) (r_{1} – r_{2})\)

=\(2 \pi (r_{1}+ r_{2}) (h + r_{1} – r_{2})\)