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Grade 7 · Math · Unit 18 of 20

Volume

Boxes, cubes and cylinders

What your child practises

Finding volume as base area × height for boxes and cylinders, working backwards to a missing dimension, and linking cm³ to millilitres and litres.

Ontario Curriculum expectation: E2.7 · volume of prisms and cylinders

How we explain it

Children can open this short lesson before they practise.

  1. Volume is the amount of space inside a 3D object.
  2. For a prism: volume = area of the base × height.
  3. Volume is measured in cubic units, like cm³.

Example: A box is 4 cm long, 3 cm wide and 2 cm high. What is its volume? Base area: 4 × 3 = 12 cm². Volume: 12 × 2 = 24. Answer: 24 cm³

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 11 cm long, 11 cm wide and 5 cm high. What is its volume?

    answer boxcm³

    Show answer

    605 cm³

    Hint: V = l × w × h = 11 × 11 × 5 = 121 × 5 = 605 cm³.

  2. Question 2

    A cube has edges 9 cm long. What is its volume?

    • 729 cm³
    • 81 cm³
    • 486 cm³
    • 108 cm³
    Show answer

    729 cm³

    Hint: All three dimensions are 9 cm: V = 9 × 9 × 9 = 729 cm³. (81 is the area of one face.)

  3. Question 3

    A cylinder's circular base has an area of 113.04 cm². The cylinder is 3 cm tall. What is its volume?

    • 116.04 cm³
    • 1064.84 cm³
    • 339.12 cm³
    • 169.56 cm³
    Show answer

    339.12 cm³

    Hint: Volume = base area × height = 113.04 × 3 = 339.12 cm³. The base area already includes π, so don't multiply by 3.14 again.

  4. Question 4

    A cylinder has a radius of 3 cm and a height of 6 cm. What is its volume? Use 3.14 for π and round to one decimal place.

    answer boxcm³

    Show answer

    169.6 cm³

    Hint: V = π × r × r × h ≈ 3.14 × 3 × 3 × 6 = 3.14 × 54 = 169.56. Rounded: 169.6 cm³.

  5. Question 5

    Which container holds more? (Use 3.14 for π.)

    ContainerShapeSize
    CanCylinderr = 4 cm, h = 7 cm
    BoxRectangular prism9 cm × 4 cm × 8 cm
    • They hold the same amount
    • The box
    • The can
    Show answer

    The can

    Hint: Can: 3.14 × 4 × 4 × 7 = 351.68 cm³. Box: 9 × 4 × 8 = 288 cm³. The can holds more.

  6. Question 6

    1000 cm³ holds 1 L. How many litres of water fill a fish tank 15 cm × 25 cm × 30 cm?

    answer boxL

    Show answer

    11.25 L

    Hint: Volume: 15 × 25 × 30 = 11250 cm³. Divide by 1000 to change to litres: 11.25 L.

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