Content - Volume of a Right Cylinder

The concept of volumes of cylinders is very important in many areas including chemical manufacturing.

Prerequisite: Understand how to calculate the volume of a prism.

Objective: Derive the formula for computing the volume of a cylinder using the formula of the volume of a prism.

Volume of a Right Cylinder

Since we know how to calculate the volume of a prism, we use a regular prism to approach a cylinder with base radius (r) and height (h): a regular prism whose base is a quadrilateral, a pentagon, a hexagon, a heptagon, an octagon, or a many-sided regular polygon. As the number of the sides increases, the perimeter of the regular polygon approaches the circumference of the circle, and the area of the base polygon approaches the base area of the cylinder. As a result, the volume of the regular prism approaches the volume of the cylinder.

Eventually, the regular prism and the cylinder fit together perfectly when the number of the sides is large enough. Since the volume of the regular prism is the product of its base area and its height, and since its base area and the cylinder base fit together perfectly, the volume of the cylinder is also the product of its base area and its height. When we express the base area using

r², the volume of the cylinder is:

V =

r²h

[Experiment] [Exercise]