Volume — NSW Year 8 Maths
How much space a solid takes up and how much a container holds, from a drink can to a rainwater tank. Six subtopics and 120 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-VOL-C-01.
Volume in NSW Year 8
Volume is the space a solid takes up and capacity is how much a container holds. Year 7 worked with rectangular prisms. In Year 8, students use \(V = Ah\) for any prism with the same cross-section all the way through, find the volume of cylinders with \(V = \pi r^2 h\), handle composite solids, pipes and holes, and convert between cubic units, millilitres, litres, kilolitres and megalitres.
The six subtopics below start with metric units for volume and capacity, then the volume of prisms and of prisms whose cross-section is made of several shapes. Cylinders and composite cylinders follow, and the topic ends with practical capacity problems about tanks, pools and rainfall. Volume is one of the 14 topics in NSW Year 8 Maths and belongs to the Measurement and Space strand (NESA outcome MA4‑VOL‑C‑01). It relies on the area formulas from Area and Perimeter, and in Stage 5 it leads to surface area and further volume work.
Subtopics
Volume: common questions
What do you learn in Volume in Year 8?
You find the volume of prisms, cylinders and solids built from them, including pipes and blocks with holes, and change between units such as \(\text{cm}^3\), mL, L, kL and ML to answer capacity questions.
How do you find the volume of a cylinder?
Multiply the area of the circular base by the height: \(V = \pi r^2 h\). A can with a radius of 4 cm and a height of 10 cm has \(V = \pi \times 4^2 \times 10 = 160\pi \approx 502.7\text{ cm}^3\), so it holds about 503 mL.
How many litres are in a cubic metre?
One cubic metre holds 1000 litres, which is 1 kilolitre. Because \(1\text{ cm}^3\) holds 1 mL, a 1 m cube, which is 100 cm along each edge, holds \(100 \times 100 \times 100 = 1\,000\,000\text{ mL}\), or 1000 L.
Which NESA outcome covers volume?
Volume sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑VOL‑C‑01, which covers right prisms, cylinders and capacity. Year 7 starts with rectangular prisms and Year 8 adds other prisms and cylinders.
What comes after volume in Year 8?
Capacity problems often bring in rates, such as a hose filling a tank at 15 L per minute. In Stage 5 students find the surface area of prisms and cylinders, and some go on to the volume of pyramids, cones and spheres.