Try sofatutor for 30 Days

Discover why over 1.6 MILLION students choose sofatutor!

Volume of Rectangular Prism Using Cubic Units

Rating

Be the first to give a rating!
The authors
Avatar
Team Digital
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

Volume of Rectangular Prism Using Cubic Units

Calculating volume is a critical skill that helps us understand how much three-dimensional space an object occupies. This is especially useful for practical tasks such as determining the amount of liquid that can fill a container, the space required to store items, or the capacity of a room. Grasping the volume of a rectangular prism is a fundamental concept in geometry that applies to both simple and complex real-world problems.

Understanding Volume of Rectangular Prism

Rectangular prisms are a type of polyhedron with six faces, all of which are rectangles. Commonly referred to as a box or cuboid, these shapes are characterized by having three dimensions: length, width, and height.

The volume of a rectangular prism is the measure of space within the prism and is calculated by multiplying the prism's length, width, and height.

What is a rectangular prism?
How do you calculate the volume of a rectangular prism?
Can volume be measured in different units?

Volume of Rectangular Prism – Example

Calculating the volume of a rectangular prism is straightforward once you know the dimensions of the object. Let's go through an example for clarity.

Find the volume of a rectangular prism with a length of 8 cm, width of 3 cm, and height of 5 cm.

  1. Identify the dimensions: Length = 8 cm, Width = 3 cm, Height = 5 cm.
  2. Apply the volume formula: Volume = Length x Width x Height.
  3. Calculate the volume: Volume = 8 cm x 3 cm x 5 cm.
  4. Result: The volume of the rectangular prism is 120 cubic centimeters.

Real-World Applications of Volume

Understanding how to calculate the volume of a rectangular prism has numerous practical applications:

  • Packaging industries use volume to determine box sizes for shipping goods.
  • In construction, volume calculations help in material estimation for concrete slabs, foundations, and walls.
  • Interior designers calculate the volume of rooms to optimize heating and cooling systems.

Volume of a Rectangular Prism – Practice

Common Mistakes to Avoid

  • Inconsistent units: Always ensure that all measurements are in the same unit before calculating volume.
  • Rounding off too early: Round off the final answer to avoid accumulation of errors.
  • Neglecting to double-check: Always verify measurements and calculations to avoid mistakes.

Volume of Rectangular Prism Using Cubic Units – Summary

Key Learnings from this Text:

  • Volume calculation is important for understanding the space occupied by three-dimensional objects.

  • The formula for the volume of a rectangular prism is Volume = Length x Width x Height.

  • Real-world applications of volume are extensive and span many industries.
  • Consistency and accuracy in measurements are crucial for correct volume determination.

Expand your skills in geometry and measurement with additional resources, interactive practice problems, and videos available on our educational platform.

Volume of Rectangular Prism – Frequently Asked Questions

What is the volume of a rectangular prism?
How do you find the volume of a rectangular prism with missing dimensions?
Can volume be negative?
Why is understanding the volume of a rectangular prism important?
What tools can help with volume calculation?
How do you calculate the volume of an irregularly shaped object?
Does changing the unit of measure change the volume?
Is it possible to calculate volume from weight?
What is the difference between volume and surface area?
How do you convert cubic units, such as from cubic centimeters to cubic meters?

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

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Volume of Rectangular Prism Using Cubic Units .
  • 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