Mathematics 7–10 · Year 8
Volume of a cylinder: formula, measuring cylinder and displacement
Measurement and space
The idea
The volume computed from πr²h agrees with the water a cylindrical container holds and with the water an equal solid displaces, tying a formula to two independent measurements.
What you need
- A rigid, straight-sided cylindrical plastic container, such as a PET jar or a plastic beaker (the worked figures use internal radius 3.5 cm and height 10.0 cm; each group measures its own)
- 500 mL plastic measuring cylinder graduated in 5 mL
- A solid cylinder that sinks in water, such as a metal cylinder from a science-room density set, with a thread tied round it for lowering
- Displacement (overflow) can and a 100 mL plastic measuring cylinder graduated in 1 mL to catch the overflow
- Vernier callipers or ruler, water, tray, cloth
How to do it
- Measure the internal diameter and height of the container to the nearest millimetre; compute πr²h.
- Fill the container to the brim from the measuring cylinder, recording the volume poured; compare with the formula.
- Measure the solid cylinder's diameter and height with the callipers and compute its volume.
- Fill the overflow can until water runs from the spout and stops. Stand the 100 mL measuring cylinder under the spout, lower the solid in fully on its thread, and read the volume of water that overflows; compare it with the formula volume.
- Extension, leading into Stage 5 Volume A: find the volume of a composite solid (a cylinder with a hole, a prism with a cylinder on top) by both methods.
What you should see
For r = 3.5 cm and h = 10.0 cm the formula gives 384.8 cm³, and the container holds 385 mL within about 5 mL (one graduation). The water that overflows when the solid goes in equals its formula volume within about 1 mL (one graduation of the 100 mL cylinder), provided no air is trapped and no drops cling to the spout; that 1 mL is a larger percentage of a small solid than of a large one. The learner knows it worked when the formula and the fill agree within about 3 per cent and the displacement agrees with the formula within one graduation.
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.
- Volume in cm³ and capacity in mL are different quantities.
- Doubling the radius doubles the volume.
- Displacement measures the mass of the object.
Safety card
Hazards
- water spills
Controls
- work over a tray
- a plastic container and plastic measuring cylinders, so no glass vessel is filled, tipped or dropped
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
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), Stage 4 Volume; page read 2026-09-22. acara_v9 is empty by decision, not by omission: ACARA v9 has no Year 8 description for the volume of a cylinder, since AC9M8M02 reaches right prisms only and cylinders first appear at Year 9 in AC9M9M01, one year above this entry; v9 records re-read 2026-09-23MA4-VOL-C-01
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.