## 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:

- 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:

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 cm^{3}

**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 *×* h *

= (12 × 2 )× 3

=24 × 3

= 72 mm^{3}

The volume of rectangular prism is 72 cubic mm or 72 mm^{3}

### 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 45^{2} 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 in^{2}.

**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 in^{3}

The volume of rectangular prism is 315 cubic inches or 315 in^{3}.

**Example 2:**

The base area and height of a rectangular prism are 20 cm^{2} and 3 cm, respectively. What is the volume of the prism?

**Solution**:

**Step 1: **The base area *b* = 20 cm^{2}

**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 cm^{3}

Volume of a rectangular prism is 60 cubic cm or 60 cm^{3}

## 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 cm ^{2}**

- 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 ft ^{2}**

Concept Map

### 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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