A hollow cylinder is a three-dimensional geometric shape characterized by its two concentric cylinders with an empty space in between. The volume of a hollow cylinder represents the amount of space enclosed by its walls. In order to determine the volume of a hollow cylinder, it is necessary to have the measurements of the inner and outer radii, along with the height of the cylinder.
To determine the volume of a hollow cylinder, we subtract the inner cylinder’s volume from the outer cylinder’s volume. The formula for the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder. Here, π (pi) is a mathematical constant approximately equal to 3.14159.
Let’s denote the radius of the outer cylinder as R and the radius of the inner cylinder as r, with the height of the cylinder being h. The volume of the hollow cylinder can be calculated as follows:
Volume of outer cylinder = πR²h
Volume of inner cylinder = πr²h
Therefore, the volume of the hollow cylinder is obtained by subtracting the volume of the inner cylinder from the volume of the outer cylinder:
V = Volume of outer cylinder – Volume of inner cylinder
V = πR²h – πr²h
V = π(R² – r²)h
Hence, the volume of the hollow cylinder with an outer radius R, inner radius r, and height h is π(R² – r²)h cubic units.