Cubic measure

Cubic measure

Lessons

In this lesson, we will learn:

  • That cubic measure refers to the cubed units that are used to measure volume
  • How to count the cubic measure of volumes for a single layer of unit cubes
  • How to count the cubic measure of volumes for multiple layers of unit cubes

Notes:

  • Cubic measure refers to the units we use to measure volume
    • A unit cube is a cube with a measure of 1 unit on each side
    • Units can be in metric units (i.e. m3, cm3, mm3) or other customary units (i.e. ft3, in3, yd3)

2D Shapes: Area and Perimeter of Rectangles

  • Recall that different dimensions (1-dimensional, 2-dimensional, 3-dimensional) correspond to geometric properties of shapes (perimeter, area, volume) as well as their units:

2D Shapes: Area and Perimeter of Rectangles
    • For the 3D property of shapes ( volume ), we use cubes to measure the amount of space occupied by a 3D shape

  • The cubic measure of volume can be thought of as the number of unit cubes that can fit in a 3D shape
    • If there is only one layer of unit cubes, simply count the number to find the cubic measure.

2D Shapes: Area and Perimeter of Rectangles

    • If there are multiple layers of unit cubes: count the number in one layer and multiply by the number of layers there are in the same direction.

2D Shapes: Area and Perimeter of Rectangles
  • Introduction
    Introduction to Cubic Measure:
    a)
    What is cubic measure?

    b)
    How to count the cubic measure of volumes for rectangular prisms


  • 1.
    Counting Cubic Units of Rectangular Prisms
    Count to find the cubic measure of each 3D shape. The unit is specified next to the shape.
    a)

    2D Shapes: Area and Perimeter of Rectangles edges are in centimeters (cm)

    b)

    2D Shapes: Area and Perimeter of Rectangles edges are in millimeters (mm)

    c)

    2D Shapes: Area and Perimeter of Rectangles edges are in kilometers (km)

    d)

    2D Shapes: Area and Perimeter of Rectangles edges are in yards (yd)


  • 2.
    Counting Shortcuts for Cubic Units of Rectangular Prisms
    Find the cubic measure of each rectangular prism.
    a)

    2D Shapes: Area and Perimeter of Rectangles edges are in meters (m)

    b)

    2D Shapes: Area and Perimeter of Rectangles edges are in inches (in)

    c)

    2D Shapes: Area and Perimeter of Rectangles edges are in feet (ft).

    d)

    2D Shapes: Area and Perimeter of Rectangles edges are in centimeters (cm)


  • 3.
    Given the front view of the rectangular prism and the total cubic measure (volume), complete a 3D drawing.
    a)
    Front View: 2D Shapes: Area and Perimeter of Rectangles Volume = 14 in3

    b)
    Front View: 2D Shapes: Area and Perimeter of Rectangles Volume = 30 yd3

    c)
    Front View: 2D Shapes: Area and Perimeter of Rectangles Volume = 24 ft3


  • 4.
    Same Cubic Measures in Different Configurations
    You will be tasked with building a regular rectangular prism with cubic centimeter blocks.
    a)
    If the total cubic measurement must be 8cm3, draw three different rectangular prisms with this volume.

    b)
    If the total cubic measurement must be 12cm3 , draw four different rectangular prisms with this volume.

    c)
    If the total cubic measurement must be 18cm3 , draw five different rectangular prisms with this volume.