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Formula Volume of a Rectangular Prism

How to find the Volume of a Rectangular Cylinder

Picture of Right Circular Cylinder

This page examines the properties of a rectangular prism such as the image on the right. A rectangular prism is exactly what it sounds like it's a 3 dimensional shape with a width, height and a length (or base) such as the 3,2, and 8 this picture on the right.

Rectangular Prism

Volume Formula

Picture of Formula of a Rectangular Prism

Practice Problems on Volume of a Rectangular Prism

Practice 1

What is the volume of the rectangular prism with the dimension shown below?

Use the formula for the volume of a cylinder as shown below.

Volume = (2)(5)(3)= 30

Practice 2

If the volume of a rectangular prism is 30 "3 and its height is 5 ", its length is 2 ", what is its width?

$$ volume = length \cdot width \cdot height \\ 30 = 5 \cdot 2 \cdot width \\ 30 = 10 \cdot width \\ width = \frac{30}{10} = 3\text{ "} $$

Practice 3

The volume of a rectangular prism is 125 "3 and its height is 5 ". Is it possible for all 3 of its dimensions (base, height, width) to be the exact same measurement? Explain

Yes, it is possible because:

$$ 5^3 = 125 \\ volume = length \cdot width \cdot height \\ 125 = 5 \cdot 5 \cdot 5 \cdot 5 $$

Practice 4

Rectangular prism A has the following dimensions: 2" width, 3 " height and 6 " base (ie length). On the other hand, rectangular prism B has these dimensions: 1 " width, 3 " height and 7" base (or length).

Which prism has a greater volume?

Prism A

$$ \\ volume = length \cdot width \cdot height \\ V = 2 \cdot 3 \cdot 6 = \color{red}{36 \text{ in}^3 } $$

Prism B

$$ volume = length \cdot width \cdot height \\ V = 1 \cdot 3 \cdot 7 = 21\text{ in}^3 $$

Answer: Prism A


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