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5th grade · Math · Unit 12 of 12

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.

Minnesota K-12 Academic Standards benchmark: 5.2.3.3; 5.2.3.5 · measuring volume with unit cubes and finding the volume of a rectangular prism

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 Minnesota

In the Minnesota K-12 Academic Standards, this is unit 12 of 12 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: Minnesota Department of Education (MDE)

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

    • 232 cubic inches
    • 227 cubic inches
    • 224 cubic inches
    • 56 cubic inches
    • 19 cubic inches

  2. Question 2

    Each layer of a box holds 13 unit cubes. There are 8 layers. How many cubes fill the box?

    • 102
    • 21
    • 117
    • 104
    • 103

  3. Question 3

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

    • cubic centimeters
    • square feet
    • inches
    • square inches

  4. Question 4

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

    • 108 cm³
    • 800 cm³
    • 118 cm³
    • 109 cm³
    • 92 cm³

  5. Question 5

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

    • 16
    • 32
    • 48
    • 10

  6. Question 6

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

    • 88 ft
    • 16 ft
    • 4 ft
    • 12 ft
    • 6 ft

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