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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.

Washington State Learning Standards learning standard: M.5.SR.MD.3; M.5.SR.MD.4; M.5.SR.MD.5 · understanding volume, measuring it with unit cubes, and using V = l × w × h, including for figures made of two boxes

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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