Volume of Cuboids, Cubes, and Cylinders

By the end of this lesson you will be able to:

• Calculate the volume of cuboids and cubes using
• Calculate the volume of cylinders using
• Convert between cm³, ml, and litres

The Vendor's Two Container Questions

A market vendor has two containers:

• A grain box: 5 cm long, 4 cm wide, 3 cm deep
• A cylindrical tin: radius 7 cm, height 10 cm

She wants to know: How much does each container hold — and what should the label in litres say?

Area Is the First Step

Recall from measurement-01:

That area tells us how many unit squares tile the bottom of the grain box.

Key question: What happens when we stack layers of unit cubes on top of that base?

Stacking Unit Layers Gives Volume

• Bottom layer: unit cubes
• Stack 3 layers: unit cubes
• Volume: — measured in cm³

Base area × height = volume

The Cube Is a Special Cuboid

When all three edges are equal:

Vendor's sugar cube: side cm

Same engine, new notation.

Three Dimensions → Cubic Units

One rule before we calculate:

Two lengths multiplied → a square unit (cm²).
Three → a cubic unit (cm³).

Worked Examples: Cuboid and Cube

Vendor's grain box — cuboid :

Vendor's sugar cube — cube side cm:

Notice: write the unit cm³ in every answer.

Check-In: Cuboid and Cube Volumes

Find the volume of each. Include the unit.

1. Cuboid:
2. Cube: side cm
3. Cuboid:

(Answers: 120 cm³ · 27 cm³ · 140 cm³)

Same Engine, New Base Shape

The grain box has a rectangular base →

What if the vendor's tin has a circular base?

The engine is the same: base area × height

We already know the area of a circle from measurement-02:

Cylinder = Stack of Circular Slices

• Stack of identical circular cross-sections, each with area

• Only is squared — is a separate factor, not raised to any power

Worked: The Vendor's Cylindrical Tin

Radius cm, height cm,

Step 1 — Base area:

Step 2 — Volume:

Worked: A Second Cylinder Example

Radius cm, height cm,

Step 1 — Base area:

Step 2 — Volume:

Find the Error: Cubing the Radius

A student writes:

What went wrong? Write your reason before reading on.

is the base area — flat, 2D. Cubing inflates the base before is multiplied in.
Square ; never cube it.

Diameter Trap: Halve It First

Check-In: Practice Finding Cylinder Volume

Find the volume of each cylinder. Show all steps. Use .

1. cm, cm → ?
2. diameter cm, cm → ?

(Answers: 5544 cm³ · 471 cm³)

The Vendor Needs a Label

The cylindrical tin holds 1540 cm³ of water.

The shelf label must say: "? litres"

How do we convert cubic centimetres to litres?

We know the volume. We do not yet know the capacity unit. That gap is what Chunk 3 closes.

Volume and Capacity Are Not the Same

The Bridge: 1 cm³ = 1 ml

Demonstration: A cube with side 10 cm

It holds 1 litre. Therefore:

A fact, not a formula — built into how litres are defined.

Worked: Labelling the Vendor's Tin

Vendor's tin:

Plausibility check first: Would a market tin hold 1540 litres? A 1540-litre container would fill a small room. That cannot be right.

Convert:

The label reads: 1.54 litres ✓

Worked: Labelling a Water Tank

A rectangular tank:

Step 1 — Volume:

Step 2 — Capacity:

The tank label reads: 10 litres

Putting Both Volume Skills Together

We can now:

1. Compute volume from dimensions (cm³)
2. Convert that volume to capacity (litres)

What real problems look like:
A drum, a tank, and a question about how many trips to the well. The question decides whether the target is cm³ or litres — read the question first.

Worked: Volume of a Water Drum

Drum: cm, cm

Base area:

Volume:

Capacity:

Worked: Decomposing an L-Shaped Tank

Split into two cuboids:

• A: →
• B: →

How Many Jerricans Can We Fill?

The water drum holds 385 litres (from Slide 22).

A standard jerrican holds 20 litres.

Question: How many full jerricans can be filled from the drum?

(Work this out completely before looking — no steps are given.)

Answer: (with 5 litres remaining)

Which Container Holds More Liquid?

A: Cuboid cm

B: Cylinder cm, cm,

1. Find each volume in cm³.
2. Convert to litres.
3. Which holds more, and by how much?

(A = 15 l · B = 15.4 l)

The Engine Behind Every Formula

1 cm³ = 1 ml — 1000 cm³ = 1 litre