Volume as additive · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Volume as additive

Mathematics · Measurement · ages 10-11
Name ______________________   Date ____________

  1. A cuboid measures 5 cm by 4 cm by 3 cm. What is its volume in cubic centimetres?

    Answer: ______________

  2. A cuboid is 4 by 3 by 2. What is its volume?

    • 9
    • 14
    • 29
    • 24

  3. What is the first step to find the volume of a composite solid made of two rectangular prisms?

    • Multiply the whole shape's outer length, width, and height
    • Split the solid into separate rectangular prisms
    • Only measure the largest prism

  4. Volume is additive, meaning you can add the volumes of non-overlapping parts to get the total volume.

    Circle one:   True   False

  5. A step structure has a bottom block 6 by 4 by 2 and a top block 4 by 4 by 2. What is the total volume?

    Answer: ______________

  6. The chart shows the volumes of two sections of a composite solid. What is the total volume?

    Section 118Section 212
    • 216 cubic units
    • 6 cubic units
    • 30 cubic units

  7. An L-shaped solid splits into cuboids of volume 24 and 36. What is the total volume?

    • 60
    • 50
    • 40
    • 12

  8. Mia models an L-shape as one solid 6 by 4 by 4 box and gets 96. The true split into parts gives 48 + 32 = 80. Is Mia's single-box method right here?

    Circle one:   True   False

  9. Jax finds the volume of an L-shaped solid by multiplying the tallest height by the widest length and widest width of the whole outline, without splitting it into prisms. What is wrong with his method?

    • He counted empty space that is not part of the solid
    • He should have divided instead of multiplied
    • Nothing, that method always works

  10. Why can you add the parts of a composite solid?

    • Volumes always double
    • Only cubes add up
    • Volumes of non-overlapping parts add to the whole
    • Addition is the only operation allowed
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Volume as additive W1-mt_5TBUFnCy5--s1

  1. 60 · The volume is 60 cubic cm because 5 times 4 times 3 equals 60.
  2. 24 · 24 is correct because 4 times 3 times 2 equals 24.
  3. Split the solid into separate rectangular prisms · Splitting the solid into prisms you know how to measure comes first. Then find each volume and add them.
  4. True · That's what additive means here: parts combine into the whole without double counting.
  5. 80 · The total is 80 because 48 plus 32 equals 80.
  6. 30 cubic units · Add the two bar values: 18 + 12 = 30 cubic units.
  7. 60 · 60 is correct because the parts add: 24 + 36 = 60.
  8. False · Mia is wrong. Her big box includes empty space the L-shape does not fill.
  9. He counted empty space that is not part of the solid · Treating the L-shape as one full box counts a chunk of empty space that isn't really part of the solid. Splitting into prisms avoids that mistake.
  10. Volumes of non-overlapping parts add to the whole · Volumes of non-overlapping parts add to the whole because each bit is counted exactly once.
Worksheet · LightMySky