Grade 6 Math · Topic 62

Volume of Rectangular Prisms

Volume is the amount of space inside a 3-D figure, measured in cubic units. For a rectangular prism, volume equals length times width times height.

Lesson alignment: 6.G.A.2 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Explore a rectangular prism

Change its dimensions and connect the layers of unit cubes to volume.

Think first: How many unit cubes do you expect in one layer before you count all the layers?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the volume of a 5 × 3 × 4 cm box.

Use the volume formula and substitute the given numbers: V = 5 × 3 × 4 = 60 cm³.

Answer: 60 cm³

Worked example 2

A cube has side 7 in. Find its volume.

Use the volume formula and substitute the given numbers: V = 7³ = 343 in³.

Answer: 343 in³

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. ℓ=4, w=3, h=2
    Check

    24

  2. ℓ=5, w=5, h=5
    Check

    125

  3. ℓ=10, w=4, h=3
    Check

    120

  4. ℓ=8, w=6, h=5
    Check

    240

  5. ℓ=12, w=3, h=2
    Check

    72

  6. Cube s = 6
    Check

    216

  7. ℓ=9, w=5, h=4
    Check

    180

  8. ℓ=15, w=10, h=8
    Check

    1200

Try this situation 1

An aquarium is 24 in long, 12 in wide, and 15 in tall. How many cubic inches of water can it hold?

Show a worked solution

Answer: 4,320 in³.

Use the volume formula and substitute the given numbers: V = 24 × 12 × 15 = 4320.

Try this situation 2

A box is 12 in × 8 in × 5 in. How many 1-inch cubes fit inside?

Show a worked solution

Answer: 480 cubes.

Use the volume formula and substitute the given numbers: V = 12 × 8 × 5 = 480. Each unit cube fills 1 in³.

Fresh questions · saved on this device

Practice this skill

16 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

Your practice results stay in this browser and appear in the course progress report.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A rectangular prism has a length of 6 cm, a width of 5 cm, and a height of 4 cm. What is the volume?

2. A rectangular cake measures 12 cm long, 8 cm wide, and 5 cm tall. A rectangular piece measuring 4 cm long, 3 cm wide, and 5 cm tall is removed. What is the volume of cake remaining?

3. A rectangular aquarium has dimensions 8 cm long, 5 cm wide, and 6 cm tall. What is the volume in cubic centimeters?

4. Two rectangular boxes are stacked on top of each other. The bottom box is 8 in long, 5 in wide, and 3 in tall. The top box is 4 in long, 5 in wide, and 2 in tall. What is the total volume?

5. A shipping box has length 7 in, width 6 in, and height 4 in. What is the volume?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗