Volume of a Rectangular Prism
Companies need to know the volume of a box in order to determine how much of their product will fit inside.
Here is an example:
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_1.png)
The volume is equal to the number of 1 in x 1 in x 1 in cubes we can fit inside this box.
There could be 15 cubes across the length by 4 across the width, making a bottom layer of 15 x 4 = 60 cubes. You can also think of this as the area of the base.
Notice that the height of the box is 8 in. That means that we could fit 8 layers of 60 cubes.
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_2.png)
In other words, the volume of this box is 480 cubic inches.
This could be simplified to the formulas V = Bh or V = l w h for all rectangular prisms.
Let's Practice! Determine the volume of each prism.
1.) ![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_3.png)
V = l w h
V = l w h
V = (4.5 cm)(3.2 cm)(4.2 cm)
V = 60.48 cm3
3.)
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_6.png)
4.)![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_7.png)
V = Bh
V = (112 in.2)(23 in.)
V = 2576 in.3
Let's Review![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_3.png)
V = l w h
V = (25 in.)(3 in.)(7 in.)
V = (75 in2)(7 in)
V = 525 in3
2.)
V = (75 in2)(7 in)
V = 525 in3
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_4.png)
V = (4.5 cm)(3.2 cm)(4.2 cm)
V = 60.48 cm3
3.)
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_5.png)
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_6.png)
4.)
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_7.png)
V = Bh
V = (112 in.2)(23 in.)
V = 2576 in.3
The volume of a prism is the space that fills it. You can determine the volume of a rectangular prism by either multiplying the area of the base times the height or by multiplying the length, width and height.
![](/math/geometry/topics/images/volume_of_a_rectangular_prism_img_8.png)
Related Links: Volume of a Rectangular Prism Worksheets Math Geometry Area of Rectangular Prism Volume of a Rectangular Prism |