Measurement — NSW Year 10 Advanced Maths
Units, accuracy, Pythagoras in 3D, and the surface area and volume of prisms, cylinders, pyramids, cones, spheres and composite solids. Thirteen subtopics and 260 practice questions, aligned to MA5-ARE-P-01 and MA5-VOL-P-01.
Measurement in NSW Year 10 Advanced
Measurement in Year 10 Advanced deals with solid objects and how accurately they can be measured. Students convert units and use scientific notation, find limits of accuracy, use Pythagoras' theorem in three dimensions, and find the surface area and volume of prisms, cylinders, pyramids, cones, spheres and composite solids, including the rule \(V=\frac{1}{3}Ah\) for pyramids and cones.
The 13 subtopics below start with converting units, accuracy of measuring instruments and Pythagoras' theorem in 3D, then move through the surface areas of prisms, cylinders, pyramids, cones and composite solids, then volume, and finish with spheres and similar solids. Measurement is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Measurement and Space strand (NESA outcomes MA5‑MAG‑C‑01, MA5‑ARE‑C‑01, MA5‑ARE‑P‑01, MA5‑VOL‑C‑01, MA5‑VOL‑P‑01, MA5‑TRG‑P‑01 and MA5‑GEO‑P‑01). These skills are used again in trigonometry and in measurement work in Year 11 and 12.
Subtopics
Measurement: common questions
What is the formula for the surface area of a cone?
A closed cone has surface area \(\pi rl+\pi r^2\), with radius \(r\) and slant height \(l\). For \(r=9\) cm and \(l=12\) cm, the area is \(108\pi+81\pi=189\pi\approx593.8~\text{cm}^2\).
Why is the volume of a cone one third of a cylinder?
A cone holds exactly one third of a cylinder with the same base and height, so \(V=\frac{1}{3}\pi r^2h\). The same rule, \(V=\frac{1}{3}Ah\), works for every pyramid.
What is the difference between slant height and perpendicular height?
The perpendicular height goes straight down from the apex to the centre of the base. The slant height runs down the middle of a sloping face. They form a right-angled triangle with half the base, so Pythagoras' theorem links them.
How do you calculate percentage error?
Percentage error is the absolute error, half the smallest unit on the scale, divided by the measurement, times 100%. A jug marked every 25 mL read at 375 mL has an absolute error of 12.5 mL, a percentage error of \(\frac{12.5}{375}\times100\%\approx3.33\%\).
Which NESA outcomes does Measurement cover?
Units and accuracy are MA5‑MAG‑C‑01, prisms and cylinders are MA5‑ARE‑C‑01 and MA5‑VOL‑C‑01, pyramids, cones, spheres and composite solids are MA5‑ARE‑P‑01 and MA5‑VOL‑P‑01, 3D Pythagoras is MA5‑TRG‑P‑01, and similar solids are MA5‑GEO‑P‑01, in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).