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5th grade · Math · Unit 14 of 14

Volume of Boxes

Cubes, layers and l × w × h

What your child practices

Finding volume by counting unit cubes and layers, using V = l × w × h, finding a missing side, and adding the volumes of two boxes.

Alaska content standards learning standard: 5.MD.5; 5.MD.6; 5.MD.7 · understanding volume, measuring it with unit cubes, and relating it to multiplication and addition

How we explain it

Children can open this short lesson before they practice.

  1. Volume counts the unit cubes that fill a solid.
  2. For a box, V = length × width × height.
  3. For two boxes stuck together, add their volumes.

Example: A box is 4 in long, 3 in wide and 2 in high. What is its volume? 4 × 3 = 12 cubes in one layer. 2 layers: 12 × 2 = 24. Answer: 24 cubic inches

Volume of Boxes in Alaska

In the Alaska content standards, this is unit 14 of 14 in 5th grade Math, after Unlike Denominators.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alaska Department of Education and Early Development

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A shape is made of two boxes: 5 × 4 × 4 and 6 × 4 × 2 (in cm). What is its total volume?

    • 138 cm³
    • 129 cm³
    • 128 cm³
    • 3840 cm³
    • 32 cm³

  2. Question 2

    A box is 7 cm long, 8 cm wide and 9 cm high. What is its volume?

    • 504 cubic centimeters
    • 382 cubic centimeters
    • 56 cubic centimeters
    • 502 cubic centimeters
    • 24 cubic centimeters

  3. Question 3

    Which unit measures volume?

    • cubic inches
    • pounds
    • square inches
    • inches

  4. Question 4

    Each layer of a box holds 12 unit cubes. There are 8 layers. How many cubes fill the box?

    • 93
    • 108
    • 96
    • 99
    • 20

  5. Question 5

    A box is 2 cubes long, 2 cubes wide and 2 cubes high. How many unit cubes fill it?

    • 4
    • 12
    • 6
    • 8

  6. Question 6

    A box has a volume of 96 cubic feet. It is 6 ft long and 4 ft wide. How high is it?

    • 8 ft
    • 4 ft
    • 86 ft
    • 6 ft
    • 24 ft

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