Rectangular Prism
Volume Formula
This page examines the properties of a rectangular prism such as the image above. 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 .
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.
$ V = 2 \cdot 5 \cdot 3 \\ V = 30 $
Practice 2
$$ volume = l \cdot w \cdot h \\ 30 = 5 \cdot 2 \cdot w \\ 30 = 10 \cdot w \\ width = \frac{30}{10} = 3\text{"} $$
Practice 3
Yes, it is possible because:
$$ 5^3 = 125 \\ volume = length \cdot width \cdot height \\ 125 = 5 \cdot 5 \cdot 5 $$
Practice 4
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
