Measurement & Data
Volume of Rectangular Prisms and Unit Conversions
Grade 5
- ✓By the end of this lesson students will be able to recognize volume as an attribute of solid figures.
- ✓By the end of this lesson students will be able to understand that a unit cube has 'one cubic unit' of volume.
- ✓By the end of this lesson students will be able to apply the formulas V = l × w × h and V = B × h to find the volume of right rectangular prisms with whole-number edge lengths.
- ✓By the end of this lesson students will be able to solve real-world and mathematical problems involving the volume of rectangular prisms.
- ✓By the end of this lesson students will be able to convert linear units of measurement (e.g., feet to inches) before calculating volume to ensure consistent units.
Key concepts
Volume is the amount of space a three-dimensional (3D) object occupies. It tells us how much 'stuff' can fit inside an object or how much space the object itself takes up. Volume is measured in cubic units.
A unit cube is a cube with a side length of 1 unit. For example, a cube with sides of 1 inch has a volume of 1 cubic inch. A cube with sides of 1 centimeter has a volume of 1 cubic centimeter. Unit cubes are used as the basic building blocks to measure the volume of larger objects.
A rectangular prism is a three-dimensional shape that has six rectangular faces. Think of a box, a brick, or a tissue box. It has a length, a width, and a height.
The volume of a rectangular prism can be found by multiplying its length, width, and height. Another way to think about it is to multiply the area of its base (length × width) by its height. The units for volume will always be cubic units (e.g., cubic inches, cubic feet, cubic centimeters).
When solving volume problems, it's important that all the dimensions (length, width, and height) are in the same unit of measurement. If they are not, you must convert one or more dimensions so that all units are consistent before you calculate the volume. For example, if length is in feet and width/height are in inches, convert the length to inches first (1 foot = 12 inches) or convert the width/height to feet.
Key facts to remember
- 1Volume is the amount of space a 3D object occupies.
- 2Volume is measured in cubic units (e.g., cubic inches, cubic feet, cubic centimeters).
- 3A unit cube has a volume of 1 cubic unit.
- 4The formula for the volume of a rectangular prism is V = length × width × height (V = l × w × h).
- 5Another formula for the volume of a rectangular prism is V = Base Area × height (V = B × h).
- 6All dimensions must be in the same unit before calculating volume.
- 7Common linear unit conversions: 1 foot = 12 inches, 1 yard = 3 feet, 1 meter = 100 centimeters.
Worked examples
Example 1
A rectangular fish tank has a length of 20 inches, a width of 10 inches, and a height of 12 inches. What is the volume of the fish tank?
Answer
The volume of the fish tank is 2400 cubic inches.
Notice that when you multiply inches by inches by inches, the unit becomes cubic inches (in³).
Example 2
A storage box is 3 feet long, 2 feet wide, and 18 inches high. What is the volume of the box in cubic feet?
Answer
The volume of the storage box is 9 cubic feet.
Always make sure your units are consistent before you start multiplying!
Example 3
A rectangular sandbox has a base area of 24 square feet. If the sand in the box is 0.5 feet deep, what is the volume of the sand?
Answer
The volume of the sand in the box is 12 cubic feet.
The base area is already given, so you don't need to find length and width separately.
Common mistakes
- ✗Confusing volume with area: Volume is for 3D objects and uses cubic units; area is for 2D shapes and uses square units.
- ✗Not using consistent units: Forgetting to convert all dimensions to the same unit before calculating volume.
- ✗Incorrectly calculating with decimals or fractions: Making errors when multiplying numbers that are not whole numbers.
- ✗Forgetting to include the correct cubic units in the final answer.
- ✗Multiplying only two dimensions instead of three (e.g., calculating l × w instead of l × w × h).
Exam tips
- ★Always read the problem carefully to identify all given dimensions and what the question is asking for (e.g., specific units).
- ★Draw a simple sketch of the rectangular prism if it helps you visualize the problem.
- ★Before you multiply, check that all your length, width, and height measurements are in the same unit. Convert if necessary!
- ★Show all your steps, including the formula you use, the substitution of values, and the final answer with correct cubic units.
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