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# Understanding Volume Concepts of a Rectangular Prism

Sep 29, 2022

## 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.

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 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:

1. Counting the number of cubes
1. Using a formula.

Example for volume by counting the number of cubes:

Let us calculate the volume of the below rectangular prism:

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:

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.

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?

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,

height = 3 cm.

Using Volume of a Rectangular Prism V = l × w ×

= (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

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:

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?

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.
• Find the volume of the figure.
• Find the volume of the rectangular prism.
• Find the volume of a rectangular prism.
• Color the base part of the rectangular prism.
• Find base area of a rectangular prism.
• Find the volume of a rectangular prism.

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.

Base area 12 ft2

### 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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