Key Concepts
- Volume of the rectangular prism
Develop a volume formula
Rectangular prism
A three-dimensional shape with six faces, in which all the faces of the prism are rectangles and opposite faces are equal to each other.
Real life examples of rectangular prism.
![Rectangular prism](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7290-1024x210.png)
What is a formula?
A formula is a rule that uses a symbol to relate two or more quantities.
Example:
c = a +b
Volume of a rectangular prism
What is a volume?
![Volume of a rectangular prism](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/2-46.png)
Volume is the number of cubic units required to pack a solid figure without gaps or over laps.
There are two methods to find the volume of rectangle prism:
- Counting the number of cubes
- Using a formula.
Example for volume by counting the number of cubes:
Let us calculate the volume of the below rectangular prism:
![Example for volume by counting the number of cubes:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7291.png)
You can see three cubes are arranged in three rows in two sets.
So, if you count the cubes, the volume will be 18 cubic units.
Example 1: Find the volume of rectangular prism.
Solution:
![solution](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/3-35.png)
The volume of bottom layer is 6 x 4 = 24 cubic units.
When we muultiply the volume of the bottom layer by 3.
The volume of the prism is 3 x 24 or 72 cubic units.
Now, we can conclude that the volume of the prism =6 × 4 × 3 = 72
Thus, the volume of the prism V = l × w × h
Using V = l × w × h formula
The volume of the rectangular prism is simply obtained by multiplying all three dimensions . length, height and width.
![Using V = l × w × h formula](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7292-1024x579.png)
the V = l × w × h
w is the base width of the rectangular prism
l is the base length of the rectangular prism
h would be height of the rectangular prism
Example 1:
Length, width and height of the base of the rectangular prism are 6 cm, 9 cm and 4 cm respectively. Find the volume of the rectangular prism?
![example 1](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/4-29.png)
Solution:
Given,
l = 6 cm
w = 9 cm
h = 4 cm
Using volume of a rectangular prism, V = l × w × h
= (6 × 9 )× 4
= 54 × 4
= 216 cm3
Example 2:
Length, width, height of the rectangular prism are 12 cm, 2 cm, and 3 cm, respectively. What is the volume of the prism?
Solution:
Let us calculate the volume of the rectangular prism using the following steps:
Given, length = 12 cm, width = 2 cm,
![example 2 solution](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/5-23.png)
height = 3 cm.
Using Volume of a Rectangular Prism V = l × w × h
= (12 × 2 )× 3
=24 × 3
= 72 mm3
The volume of rectangular prism is 72 cubic mm or 72 mm3
Using V = B × h formula
Formula of a volume of the rectangular prism is V= B × h
![Using V = B × h formula](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/6-23.png)
Example 1:
The base area and height of a rectangular prism are 452 in and 7 in, respectively. What is the volume of the prism?
Solution:
Let us calculate the volume of the rectangular prism using the following steps:
![example 1 solution](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/7-19-1024x684.png)
Step 1: The base area b = 45 in2.
Step 2: Height of the prism is 7 inches.
Step 3: Volume of the given rectangular prism V = B × h
base area × height
= 45 × 7
= 315 in3
The volume of rectangular prism is 315 cubic inches or 315 in3.
Example 2:
The base area and height of a rectangular prism are 20 cm2 and 3 cm, respectively. What is the volume of the prism?
![example 2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/8-13.png)
Solution:
Step 1: The base area b = 20 cm2
Step 2: Height of the prism is 3 cm.
Step 3: The volume of the given rectangular prism
V = B × h
base area × height
= 20 × 3
= 60 cm3
Volume of a rectangular prism is 60 cubic cm or 60 cm3
Exercise
- The length, width, and height of a rectangular prism are 15 cm, 10 cm, and 5 cm,
respectively. What is the volume of the prism? - Find the volume of rectangular prism.
![exercise 2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-50.png)
- Find the volume of the figure.
![exercise 3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/2-47.png)
- Find the volume of the rectangular prism.
![exercise 4](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/3-36.png)
- Find the volume of a rectangular prism.
![exercise 5](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/4-30.png)
- Color the base part of the rectangular prism.
![exercise 6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/5-24.png)
- Find base area of a rectangular prism.
![exercise 7](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/6-24.png)
- Find the volume of a rectangular prism.
![exercise 8](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/7-20.png)
Base area 12 cm2
- Find the volume of a fish tank that is 8 feet long and 5 feet wide, and the height is
5 feet. - Find the volume of an aquarium.
![exercise 10](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/8-14.png)
Base area 12 ft2
Concept Map
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7295-1024x421.png)
What have we learned
- Understanding the formula, volume and rectangular prism.
- How to find volume of rectangular prism by counting the cubes?
- How to find volume of rectangular prism using the formula (V) =1 x b x h.
- How to find volume of rectangular prism using the formula (V) = B x h.
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