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Cubes

  • Cubes

    Grade: 3rd to 5th

    Fill a box with cubes, rows of cubes, or layers of cubes. The number of unit cubes needed to fill the entire box is known as the volume of the box. Can you determine a rule for finding the volume of a box if you know its width, depth, and height?

    This interactive is optimized for your desktop and tablet.

    Activity

    Instructions

    Objective

    • Find the surface area and volume of each box.
      • By clicking on the flattened sides of the box, you can see what the box looks like when the sides are folded up.

     How to Use

    • Along the left side, click on a cube, a row of cubes, or a layer of cubes to fill the box.
    • The Undo button takes away the last piece you placed in the box; the Clear button removes all of the pieces from the box.
    • Use the Customize wheel to change the width, depth, and height to see boxes of various sizes. 20 is the maximum width, depth, and height.
    • You can also randomize the dimensions by clicking on the Next arrow.

     

    Exploration

    Consider the following questions:

    • How many unit cubes are needed to fill a box that measures 3 × 5 × 7?
    • How many squares are needed to cover that box?
    • What about the volume and surface area of a box that measures 5 × 7 × 3?
    • What is the volume and surface area of a box that measures 7 × 3 × 5?

    In general, how can you find the volume of a box if you know the width, depth, and height?

    How about its surface area?

    Objectives and Standards

    NCTM Standards and Expectations
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • Apply geometric concepts in modeling situations
    • 3-5
    • Geometry
    • Measurement