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5th grade · Math · Unit 9 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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 5.4(G); 5.6(A); 5.6(B) · unit cubes and the volume of rectangular prisms

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 9 of 15 in 5th grade Math, after Parentheses & Expressions and before Area & Perimeter.

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: Texas Education Agency (TEA)

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 6 cm long, 8 cm wide and 9 cm high. What is its volume?

    • 48 cubic centimeters
    • 348 cubic centimeters
    • 434 cubic centimeters
    • 23 cubic centimeters
    • 432 cubic centimeters

  2. Question 2

    Which unit measures the volume of a box?

    • cubic feet
    • inches
    • square inches
    • square feet

  3. Question 3

    A shape is made of two boxes: 3 × 5 × 2 and 3 × 3 × 2 (in cm). What is its total volume?

    • 12 cm³
    • 48 cm³
    • 58 cm³
    • 540 cm³
    • 49 cm³

  4. Question 4

    A box is 2 cubes long, 4 cubes wide and 2 cubes high. How many unit cubes fill it?

    • 17
    • 8
    • 16
    • 24

  5. Question 5

    A box has a volume of 144 cubic feet. It is 9 ft long and 2 ft wide. How high is it?

    • 5 ft
    • 16 ft
    • 8 ft
    • 18 ft
    • 133 ft

  6. Question 6

    Each layer of a box holds 20 unit cubes. There are 3 layers. How many cubes fill the box?

    • 80
    • 62
    • 58
    • 23
    • 60

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