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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.

Arizona Academic Standards learning standard: 5.MD.C.3; 5.MD.C.4; 5.MD.C.5 · 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 Arizona

In the Arizona Academic 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: Arizona Department of Education

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

    • 350 cubic centimeters
    • 441 cubic centimeters
    • 23 cubic centimeters
    • 63 cubic centimeters
    • 442 cubic centimeters

  2. Question 2

    A box is 4 cubes long, 3 cubes wide and 3 cubes high. How many unit cubes fill it?

    • 10
    • 36
    • 48
    • 12

  3. Question 3

    A shape is made of two boxes: 6 × 4 × 2 and 3 × 4 × 3 (in cm). What is its total volume?

    • 12 cm³
    • 1728 cm³
    • 84 cm³
    • 94 cm³
    • 81 cm³

  4. Question 4

    Each layer of a box holds 8 unit cubes. There are 3 layers. How many cubes fill the box?

    • 11
    • 32
    • 27
    • 22
    • 24

  5. Question 5

    A box has a volume of 32 cubic feet. It is 2 ft long and 4 ft wide. How high is it?

    • 5 ft
    • 8 ft
    • 7 ft
    • 4 ft
    • 26 ft

  6. Question 6

    Which unit tells how much space is inside a fish tank?

    • cubic inches
    • pounds
    • square inches
    • inches

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