Volume of Prisms and Cylinders

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Author: Leif Park Jordan

Description:

Derive and apply the formula for finding the volume of prisms and cylinders, being sure to discuss units.
Provide practice examples solving for the volume of prisms and cylinders, reviewing how to report answers in terms of pi () for cylinders

This packet should help a learner seeking to understand how to find the volume of prisms and cylinders.

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Tutorial

Volume of a Cube

This video explains how to find the volume of a cube.

Source: JoeBaxter on Guaranteach

Volume of a Right Rectangular Prism

This video explains how to find the volume of a rectangular prism.

Source: JoeBaxter on Guaranteach

Volume of Other Prisms

This video explains how to find the volume of prisms other than right rectangular prisms.

Volume of a Right Circular Cylinder

This video explains how to find the volume of a right circular cylinder.

Source: JoeBaxter on Guaranteach

Derivation of the Formula for the Volume of a Cylinder

Once one understands how to find the volume of a prism, the derivation of the volume of a cylinder is fairly trivial. Cylinders are, essentially, just prisms with a circular base, so finding the volume of a cylinder is just like finding the volume of a cylinder.

The formula for the volume of a prism is V = B * h, where V is volume, B is the area of the base, and h is the height of the prism. The base of a cylinder is a circle, which has area πr². Height, obviously, is the same in a cylinder as it is in a prism. By substituting πr² for B in the formula for the volume of a prism, we arrive at the formula for the volume of a cylinder:

V = πr²h.

Comparison Between Cylinders and Prisms