Surface Area and Volume — NSW Year 9 Core Maths
Metric units, accuracy, composite areas, circles, and the surface area and volume of prisms and cylinders. Eight subtopics and 160 practice questions with worked solutions, aligned to MA5-ARE-C-01 and MA5-VOL-C-01.
Surface Area and Volume in NSW Year 9
This topic is about measuring space accurately: how much material covers a solid and how much it holds. Year 9 Core students first sharpen the tools, converting metric units (including square and cubic units) and judging how accurate a measurement is. They then revise the area of composite shapes, quadrilaterals and circles, and use those areas to work out the surface area of prisms and cylinders and their volume, using \(V = Ah\) and \(V = \pi r^2 h\).
The eight subtopics below run from metric units and limits of accuracy, through composite shapes, quadrilaterals and circular shapes, to the surface area of prisms, the surface area of cylinders, and volumes of prisms and cylinders. Surface Area and Volume is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Measurement and Space strand. Its outcomes are MA5‑MAG‑C‑01 for units and accuracy, MA4‑ARE‑C‑01 for the area revision, MA5‑ARE‑C‑01 for surface area and MA5‑VOL‑C‑01 for volume. Pyramids, cones and spheres follow in later Stage 5 work.
Subtopics
Surface Area and Volume: common questions
How do you convert square and cubic units?
Square or cube the length conversion factor. Since \(1\) m \(= 100\) cm, \(1~\text{m}^2 = 100^2 = 10\,000~\text{cm}^2\) and \(1~\text{m}^3 = 100^3 = 1\,000\,000~\text{cm}^3\). Dividing by only \(100\) is the most common mistake.
What is the limit of accuracy of a measurement?
It is half the smallest unit on the measuring instrument. A ruler marked in millimetres has a limit of accuracy of \(\pm 0.5\) mm, so a reading of \(46\) mm means the true length is between \(45.5\) mm and \(46.5\) mm.
What is the formula for the surface area of a cylinder?
A closed cylinder has surface area \(A = 2\pi r^2 + 2\pi rh\): two circular ends plus the curved surface, which unrolls into a rectangle \(2\pi r\) wide and \(h\) tall. Leave out one or both ends for an open can or a pipe.
How do you work out the volume of a prism?
Multiply the area of the cross-section by the length: \(V = Ah\). A prism \(12\) cm long with a trapezium cross-section of area \(28~\text{cm}^2\) has volume \(28 \times 12 = 336~\text{cm}^3\). For a cylinder the cross-section is a circle, so \(V = \pi r^2 h\).
Which NESA outcomes cover surface area and volume in Year 9?
Surface area of prisms and cylinders is Stage 5 Core content under MA5‑ARE‑C‑01, and volume of prisms, cylinders and composite solids under MA5‑VOL‑C‑01. Units, prefixes and accuracy come under MA5‑MAG‑C‑01, and the composite area work revises the Stage 4 outcome MA4‑ARE‑C‑01.