Volume of Rectangular Prism Using Cubic Units

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Volume of Rectangular Prism Using Cubic Units

CCSS.MATH.CONTENT.5.MD.C.3.A

Basics on the topic Volume of Rectangular Prism Using Cubic Units

How do you find the volume of rectangular prisms with cubic units? Find out with this video!

Transcript Volume of Rectangular Prism Using Cubic Units

In a bustling insect world where the ant population was booming, an industrious contractor took on a remarkable challenge: constructing an apartment complex for the growing ant community. Armed with blueprints, the contractor was tasked with determining the space's volume and ensuring that each apartment would accommodate the growing number of ants. He will need to find the volume of rectangular prisms using unit cubes. A rectangular prism is a three-dimensional shape with six faces, all rectangles. The volume of a rectangular prism refers to the measurement of the space inside the shape, specifically the capacity, or how much it can hold. A cubic unit measures a figure's three sides: its length, width, and height. Each side has a measurement of one cubic unit. We can determine the volume of a rectangular prism by counting the number of cubes that fill the space. Let's find the volume of this shape. First, let's see how many unit cubes are along the length of the prism. There are three. Next, count how many units are along the width. There are five. Now, count the number of cubes that make up the height. Four. We can split this prism into the layers by this height, and see that each layer has the same amount. To find the volume we can count the number of cubes in one layer and multiply that by the number of layers. We call this layer the base of the prism. How many cubic units are in the base? Fifteen. Multiply fifteen by four. Sixty. This prism has the volume of sixty cubic units. Here are some examples to try on your own, pausing the video whenever you need extended time. What is the volume of this rectangular prism? Here, the length is two cubic units. Width is four. And height is two. The volume is sixteen cubic units. What is the volume of this rectangular prism? The length is two, width is five, and length is three. The volume is thirty cubic units. Match the rectangular prisms with their volume. Number one is , C. Two is A. Three is D, and four is B. At the job site, the diligent ants use cubic units to measure the volume of space. This helps them determine how many ants can fill each area within the apartment complex, ensuring a comfortable living environment for their community.

Volume of Rectangular Prism Using Cubic Units exercise

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What is the volume of this rectangular prism?
Hints

To find the volume, we must multiply the length by the width by the height.
Count the cubes along each side to find these measurements.

Here we can see the length is 4 units, the width is 5 units and the height is 6 units.
Multiply 4 x 5 x 6 to find the volume.

Solution
The correct answer is 120 cubic units.
- The length of the rectangular prism is 4 units.
- The width of the rectangular prism is 5 units.
- The height of the rectangular prism is 6 units.
To find the volume we must multiply the length by the width by the height.
4 x 5 x 6 = 120
Can you find the volume of each rectangular prism?
Hints
Remember, to find the volume we use this formula.
- $V$ = volume
- $l$ = length
- $w$ = width
- $h$ = height
Count the blocks on each rectangular prism to find the length, width and height.

For this rectangular prism, the length is 5 units, the height is 1 unit and the width is 3 units. Multiply these together to find the volume.
Solution
Volume of A = 15 cubic units
- length = 5 units
- height = 1 unit
- width = 3 units
- 5 x 1 x 3 = 15
Volume of B = 42 cubic units
- length = 7 units
- height = 3 unit
- width = 2 units
- 7 x 3 x 2 = 42
Volume of C = 54 cubic units
- length = 6 units
- height = 3 unit
- width = 3 units
- 6 x 3 x 3 = 54
Volume of D = 24 cubic units
- length = 8 units
- height = 1 unit
- width = 3 units
- 8 x 1 x 3 = 24
What is the volume of these rectangular prisms?
Hints

Use this formula to find each volume where $l$ = length, $w$ = width and $h$ = height.

You could draw out a rectangular prism if it helps you.
For example, we could use this one to find the volume for the prism with the length of 5 units, width of 3 units and height of 2 units.

Solution
Volume of 30 cubic units
length = 5 units; width = 3 units; height = 2 units
- 5 x 3 x 2 = 30
length = 10 units; width = 3 units; height = 1 units
- 10 x 3 x 1 = 30
Volume of 48 cubic units
length = 6 units; width = 4 units; height = 2 units
- 6 x 4 x 2 = 48
length = 4 units; width = 3 units; height = 4 units
- 4 x 3 x 4 = 48
Volume of 84 cubic units
length = 7 units; width = 3 units; height = 4 units
- 7 x 3 x 4 = 84
length = 7 units; width = 6 units; height = 2 units
- 7 x 6 x 2 = 84
Can you order these prisms?
Hints

Use this formula to find each volume where $l$ = length, $w$ = width and $h$ = height.

You could draw out a rectangular prism if it helps you.
For example, we could use this one to find the volume for the prism with the length of 7 units, width of 4 units and height of 2 units.

Work out all of the volumes and then order the measurements from smallest to biggest.

Solution
1.) $l$ : 6 units, $w$ : 1 unit, $h$ : 5 units
- 6 x 1 x 5 = 30
2.) $l$ : 6 units, $w$ : 4 units, $h$ : 2 units
- 6 x 4 x 2 = 48
3.) $l$ : 7 units, $w$ : 4 units, $h$ : 2 units
- 7 x 4 x 2 = 56
4.) $l$ : 5 units, $w$ : 4 units, $h$ : 3 units
- 5 x 4 x 3 = 60
5.) $l$ : 8 units, $w$ : 3 units, $h$ : 6 units
- 8 x 3 x 6 = 144
What is the volume of the rectangular prism?

Hints

Multiply the length by the width by the height to find the volume.

The length is 4 units.
The width is 3 units.
The height is 2 units.
Multiply these together to find the volume.

Solution

The correct answer is 24 cubic units.
The length is 4 units.
The width is 3 units.
The height is 2 units.
4 x 3 x 2 = 24
How many cereal boxes will fit into the box?

Hints

First work out the volume of one cereal box.
20 x 5 x 30 = ?

Next work out the volume of the larger box.
60 x 20 x 40 = ?
To make this calculation easier, solve 6 x 2 x 4 and then add three zeros back on.

Now divide the volume of the larger box by the volume of one cereal box.

Solution

The correct answer is 16 cereal boxes.
The volume of one cereal box is 20 x 5 x 30 = 3,000 centimetres cubed
The volume of the larger box is 60 x 20 x 40 = 48,000 centimetres cubed
48,000 $\div$ 3,000 = 16