Geometry · Surface area & volume · 4.1

Volume of a box.

Volume measures the space inside a solid, in cubic units. A rectangular prism (box) holds length × width × height unit cubes. A 3 × 4 × 5 box has volume 60.

01 / THE IDEA

See it work.

The figure

See the shape.

345

Watch the method

Volume of a box

Volume of a box = l × w × h.

1 / 2
1

Volume of a box

Volume of a rectangular prism is length × width × height.

l×w×hl \times w \times h
2

Multiply

Multiply all three dimensions.

3×4×5=603\times 4\times 5 = 60
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Find the measure.

Type the number — units optional.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

Stack the cubes

Volume fills the solid with unit cubes: layers of l × w, stacked h high.

Why it works

Area of the base × height.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Volume of a 8×7×5 box?

1

Volume of a box

Volume of a rectangular prism is length × width × height. l × w × h

2

Multiply

Multiply all three dimensions. 8× 7× 5 = 280

EX 2medium

Volume of a 6×2×9 box?

1

Volume of a box

Volume of a rectangular prism is length × width × height. l × w × h

2

Multiply

Multiply all three dimensions. 6× 2× 9 = 108

EX 3hard

Volume of a 4×5×7 box?

1

Volume of a box

Volume of a rectangular prism is length × width × height. l × w × h

2

Multiply

Multiply all three dimensions. 4× 5× 7 = 140

04 / COMMON TRAPS

Where students slip.

Trap

Using only two dimensions.

Fix

Volume needs all three: l, w, h.

Trap

Forgetting cubic units.

Fix

Volume is in cubic units.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Volume of a 5×6×4 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
C2

Volume of a 7×6×5 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
C3

Volume of a 4×3×8 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
C4

Volume of a 4×2×5 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
Apply

Apply (4)

A1

Volume of a 7×9×7 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
A2

Volume of a 4×7×3 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
A3

Volume of a 6×5×8 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
A4

Volume of a 6×9×7 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
Extension

Extension (4)

E1

Volume of a 8×6×2 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
E2

Volume of a 7×5×7 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
E3

Volume of a 6×8×6 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.
E4

Volume of a 3×4×3 box?

Need a hint?
  • Multiply l × w × h.
  • It’s base area × height.