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5th grade · Math · Unit 14 of 15

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.

California Content Standards learning standard: 5.MD.3; 5.MD.4; 5.MD.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

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 7 in long, 4 in wide and 6 in high. What is its volume?

    • 188 cubic inches
    • 166 cubic inches
    • 28 cubic inches
    • 17 cubic inches
    • 168 cubic inches

  2. Question 2

    Which unit measures volume?

    • inches
    • cubic feet
    • pounds
    • square feet

  3. Question 3

    Each layer of a box holds 10 unit cubes. There are 6 layers. How many cubes fill the box?

    • 16
    • 63
    • 70
    • 60
    • 57

  4. Question 4

    A box is 2 cubes long, 3 cubes wide and 2 cubes high. How many unit cubes fill it?

    • 6
    • 7
    • 18
    • 12

  5. Question 5

    A box has a volume of 150 cubic feet. It is 5 ft long and 5 ft wide. How high is it?

    • 6 ft
    • 25 ft
    • 7 ft
    • 140 ft
    • 12 ft

  6. Question 6

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

    • 57 cm³
    • 70 cm³
    • 60 cm³
    • 12 cm³
    • 864 cm³

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