Mathematics K–6 · Years 5–6

Cubic centimetres, litres and displacement

Measurement and space

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

A cube 10 cm on each side holds 1000 cubic centimetres, which is one litre, and the volume of a solid object can be found from the water it pushes aside.

What you need

base-10 materials: 10 hundred-flats and a thousand-cube, plus 100 centimetre cubes
a 1 L measuring jug and a 250 mL plastic measuring cylinder marked in 5 mL steps
a rectangular eraser about 2 cm by 2 cm by 5 cm that sinks in water, a small stone and a golf ball
a plastic cup that can be filled to the brim, standing in a clean tray, for the overflow method
a 1 L clear box or a cube-shaped container with 10 cm inside edges, and water

How to do it

Stack 10 flats to make the thousand-cube. Count the cubes in one flat (10 by 10) and in the stack (10 flats), and record 1000 cubic centimetres.
Fill the 10 cm box with water using the jug, reading the volume poured. Record that the box takes 1 L.
Measure the eraser with a ruler and calculate its volume. Half fill the cylinder, read the level, lower the eraser in on a thread, and read the new level. Subtract.
Find the volume of the stone and the golf ball by overflow: fill the cup to the brim in the empty tray, lower the object in on a thread, then pour the water that overflowed into the tray into the measuring cylinder and read it.
Build 36 cubic centimetres from centimetre cubes in as many different rectangular prisms as you can, recording the three dimensions each time.

What you should see

The stacked flats show 10 by 10 by 10, 1000 cubic centimetres, and the 10 cm box takes 1000 mL, so 1 cubic centimetre is 1 mL and 1 litre is 1000 cubic centimetres. An eraser measuring 2 cm by 2 cm by 5 cm has volume 20 cubic centimetres and raises the cylinder level by 20 mL within the 5 mL reading step. A golf ball (diameter 42.7 mm) pushes out about 41 mL (four thirds times pi times 2.135 cubed is 40.8 cubic centimetres), a little less if some overflow is lost on the tray. The 36-cube prisms come in 8 different sets of dimensions, from 36 by 1 by 1 to 4 by 3 by 3.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A litre and a cubic centimetre are unrelated units.
Heavier objects displace more water than lighter objects of the same size.

Safety card

Low riskLearners carry it out

Hazards

water spills
glass measuring cylinder

Controls

use plastic cylinders; work over a tray

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-3DS-02 MAO-WM-01
Australian Curriculum v9AC9M5M01AC9M6M01

Sources

The pages the author read to write this activity.

All Concept Studio activities