P5 Volume: Cuboids, Litres and Triangle Area

Nadia's goldfish, Goldie, has outgrown her little round bowl. She turns back and forth, because there is nowhere to swim. Behind her, a new glass tank draws itself on, edge by edge. "Nadia's goldfish needs a bigger tank. Let's work it out."

That is Tank Rescue, one of our Primary 5 Topic Explainers. In 30 seconds, one tank carries three questions: how big it is, how much water goes in, and the area of a triangle sticker on the back glass. Watch it first, then read on for the method behind each one.

Tank Rescue: build it, fill it, work it out.

All three questions come from Primary 5 Area and Volume in the Singapore syllabus: the volume of a cuboid, the volume of liquid in a rectangular tank, the link between litres and cubic centimetres, and the area of a triangle.

The method

Volume of a cuboid: length × width × height

A cuboid is a box shape: six rectangular faces, like a tank, a shoebox or a pencil box. Its volume is how much space it takes up, counted in cubes.

Picture the bottom of the tank covered with centimetre cubes in one flat layer. The number of cubes in that layer is length × width. Then stack layers until you reach the top. The number of layers is the height. So:

Volume = length × width × height

The answer is in cubic centimetres, written cm³, because we are counting centimetre cubes.

Water in a tank: use the water's height

Water in a rectangular tank is also a cuboid. It has the same length and width as the tank, but its height is the height of the water, not the height of the tank. That one change is where most slips happen.

Litres and cubic centimetres

Two facts link the units:

1 ml = 1 cm³
1 ℓ = 1000 ml = 1000 cm³

So to change cubic centimetres into litres, divide by 1000.

Area of a triangle: ½ × base × height

A triangle is exactly half of a rectangle with the same base and height. So:

Area of a triangle = ½ × base × height

The height must be the straight-up distance from the top of the triangle to its base, meeting the base at a right angle. It is not the length of a sloping side.

Worked examples

All the numbers below are the ones in the video. Large numbers use a space between thousands, as Singapore textbooks do.

Example 1: How big is the tank?

Nadia's new tank is 40 cm long, 25 cm wide and 30 cm tall. What is its volume?

Step 1: Find one layer. 40 × 25 = 1000. One layer of centimetre cubes on the bottom holds 1000 cubes.

Step 2: Stack the layers. The tank is 30 cm tall, so there are 30 layers: 1000 × 30 = 30 000.

The volume of the tank is 30 000 cm³.

Notice the order. Multiplying 40 by 25 first gives a round 1000, which makes the next step easy. Encourage your child to look for a friendly pair before multiplying.

Example 2: How much water?

Marcus fills it with water to a height of 20 cm. How many litres of water is that?

Step 1: Find the volume of the water. Same length and width, but the water's height is 20 cm: 40 × 25 × 20 = 20 000 cm³.

Step 2: Change the units. 1 ml = 1 cm³, so 20 000 cm³ is 20 000 ml. Then 1 ℓ = 1000 ml, so 20 000 ÷ 1000 = 20.

There are 20 ℓ of water in the tank.

Example 3: The hill sticker

A hill sticker goes on the back glass. Its base is 40 cm and its height is 15 cm. What is its area?

Step 1: Take half of the base. ½ × 40 = 20.

Step 2: Multiply by the height. 20 × 15 = 300.

The area of the sticker is 300 cm².

Area is measured in square centimetres (cm²), because we are covering a flat surface. Volume is in cubic centimetres (cm³), because we are filling a space.

Try one at home

How much more water is needed to fill Nadia's tank to the top?

The full tank holds 30 000 cm³ and the water is 20 000 cm³, so 30 000 − 20 000 = 10 000 cm³ more is needed. That is 10 000 ÷ 1000 = 10 ℓ. Another way: the empty part is 10 cm tall, so 40 × 25 × 10 = 10 000 cm³. Both ways give 10 ℓ.

Common mistakes

Adding the lengths instead of multiplying. 40 + 25 + 30 = 95 is not a volume. Ask, "How many cubes cover the bottom? How many layers?"
Using the tank's height for the water. The water is 20 cm deep, not 30 cm. Underline the water height in the question before starting.
Dividing by 100 instead of 1000. 20 000 cm³ is 20 ℓ, not 200 ℓ. Remind your child that a litre is 1000 cubic centimetres: a 1-litre carton of milk.
Forgetting the half in a triangle. 40 × 15 = 600 is the area of the whole rectangle around the sticker. The triangle is half of it.
Using a sloping side as the height. The height of a triangle always meets the base at a right angle.
Mixing up the units. cm for length, cm² for area, cm³ for volume. Say the unit aloud with every answer.

Parent tips

Find cuboids at home. A tissue box, a cereal box, a fridge drawer. Measure one together with a ruler and work out its volume.
Fill something real. Use a measuring jug to pour 1 litre of water into a rectangular container. Measure how high the water rises. It makes "1 ℓ = 1000 cm³" something your child has seen.
Draw the tank first. Ask for a quick sketch with the measurements labelled before any working. A labelled drawing catches most height mix-ups.
Fold the triangle. Cut a rectangle from paper, draw a diagonal and cut along it. Two equal triangles from one rectangle show why the half is there.
Work it out by hand. Writing the steps down, rather than doing them in the head, makes slips easy to spot. Our post on the scratch pad and showing your working has more on this habit.

If your child is working through other Primary 5 topics, our guide to Primary 5 sample questions explained walks through more examples.

How Singapore Math Drills supports the habit

Near the end of the video, a small box sketches itself on a ruled sheet and "40 × 25 × 30" writes itself in. "Like to work it out by hand? Use the built-in scratch pad, right in the app."

Built-in scratch pad: a full-screen canvas so your child can work a problem out by hand without leaving the app, with colours, line widths and ruled lines.
Progressive hints and worked solutions: every question can be opened up step by step, and every question has a full worked solution to read afterwards.
Daily Five drills: five hand-picked drill cards are waiting each day, so volume and area come back regularly without any planning.

Build it, fill it, work it out.

Try a sample

Try a free interactive Primary 5 worksheet and see how calm practice feels, with no signup or credit card required.

Try a free Singapore math sample