Geometry · Apply · 5.2

Tanks & containers.

How much a container holds — water in a tank, sand in a box — is a volume problem: length × width × height gives the cubic units. A 4 × 3 × 6 tank holds 72 cubic units.

01 / THE IDEA

See it work.

The figure

See the shape.

436

Watch the method

Tanks & containers

Capacity → volume = 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.

4×3×6=724\times 3\times 6 = 72
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.

Fill the space

Capacity is the volume — the cubic units a solid contains.

Why it works

Pour it full.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Volume of a 6×4×9 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× 4× 9 = 216

EX 2medium

Volume of a 8×7×9 box?

1

Volume of a box

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

2

Multiply

Multiply all three dimensions. 8× 7× 9 = 504

EX 3hard

Volume of a 7×9×3 box?

1

Volume of a box

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

2

Multiply

Multiply all three dimensions. 7× 9× 3 = 189

04 / COMMON TRAPS

Where students slip.

Trap

Using area for capacity.

Fix

How much it holds is volume (three dimensions).

Trap

Dropping a dimension.

Fix

Use length, width, AND height.

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 5×3×5 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
C2

Volume of a 8×5×2 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
C3

Volume of a 9×5×9 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
C4

Volume of a 8×3×3 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
Apply

Apply (4)

A1

Volume of a 6×7×8 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
A2

Volume of a 5×6×5 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
A3

Volume of a 4×4×8 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
A4

Volume of a 4×6×3 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
Extension

Extension (4)

E1

Volume of a 9×4×9 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
E2

Volume of a 7×9×5 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
E3

Volume of a 4×4×3 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.
E4

Volume of a 7×7×2 box?

Need a hint?
  • Capacity → volume.
  • Multiply all three dimensions.