Learn on PengiIllustrative Mathematics, Grade 5Chapter 1: Finding Volume

Lesson 4: Cubic Units of Measure

In this Grade 5 Illustrative Mathematics lesson from Chapter 1: Finding Volume, students learn to measure the volume of rectangular prisms using standard cubic units including cubic centimeters, cubic inches, and cubic feet. Students apply the formulas length × width × height and base × height to calculate volume in real-world contexts, such as finding the volume of a moving truck. The lesson also develops students' understanding of how to choose an appropriate unit of measure depending on the size of the object being measured.

Section 1

Introduction to Volume and Cubic Units

Property

Volume is a measure of how much space is inside a three-dimensional object or how much it takes to fill a container.
Volume is always measured in cubic units such as cubic inches (in3\text{in}^3), cubic feet (ft3\text{ft}^3), cubic centimeters (cm3\text{cm}^3), or cubic meters (m3\text{m}^3).

Examples

Section 2

Calculating Volume with Standard Units

Property

The volume (VV) of a rectangular prism is found by multiplying its length (ll), width (ww), and height (hh). The unit of volume is a cubic unit, derived from the unit of length.

V=l×w×hV = l \times w \times h

Examples

  • A box with a length of 5 cm5 \text{ cm}, a width of 2 cm2 \text{ cm}, and a height of 3 cm3 \text{ cm} has a volume of:
V=5 cm×2 cm×3 cm=30 cm3V = 5 \text{ cm} \times 2 \text{ cm} \times 3 \text{ cm} = 30 \text{ cm}^3
  • A cube with a side length of 4 inches4 \text{ inches} has a volume of:
V=4 in×4 in×4 in=64 in3V = 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} = 64 \text{ in}^3

Explanation

Volume measures the total amount of space inside a three-dimensional object. To calculate it, you multiply the object''s three dimensions: length, width, and height. The unit of measurement for volume is always "cubic," such as cubic centimeters (cm3\text{cm}^3) or cubic feet (ft3\text{ft}^3). This tells us how many cubes of a specific size (e.g., a 1 cm by 1 cm by 1 cm cube) would be needed to fill the object completely.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Introduction to Volume and Cubic Units

Property

Volume is a measure of how much space is inside a three-dimensional object or how much it takes to fill a container.
Volume is always measured in cubic units such as cubic inches (in3\text{in}^3), cubic feet (ft3\text{ft}^3), cubic centimeters (cm3\text{cm}^3), or cubic meters (m3\text{m}^3).

Examples

Section 2

Calculating Volume with Standard Units

Property

The volume (VV) of a rectangular prism is found by multiplying its length (ll), width (ww), and height (hh). The unit of volume is a cubic unit, derived from the unit of length.

V=l×w×hV = l \times w \times h

Examples

  • A box with a length of 5 cm5 \text{ cm}, a width of 2 cm2 \text{ cm}, and a height of 3 cm3 \text{ cm} has a volume of:
V=5 cm×2 cm×3 cm=30 cm3V = 5 \text{ cm} \times 2 \text{ cm} \times 3 \text{ cm} = 30 \text{ cm}^3
  • A cube with a side length of 4 inches4 \text{ inches} has a volume of:
V=4 in×4 in×4 in=64 in3V = 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} = 64 \text{ in}^3

Explanation

Volume measures the total amount of space inside a three-dimensional object. To calculate it, you multiply the object''s three dimensions: length, width, and height. The unit of measurement for volume is always "cubic," such as cubic centimeters (cm3\text{cm}^3) or cubic feet (ft3\text{ft}^3). This tells us how many cubes of a specific size (e.g., a 1 cm by 1 cm by 1 cm cube) would be needed to fill the object completely.