Surface Area and Volume — NSW Year 9 Advanced Maths
Units and measurement error, areas of composite and circular shapes, and surface area and volume. Ten subtopics and 200 questions with worked solutions, aligned to NESA outcomes MA5-ARE-C-01, MA5-VOL-C-01 and MA5-MAG-C-01.
Surface Area and Volume in NSW Year 9 Advanced
Surface Area and Volume measures the space a shape covers and the space a solid fills. Year 9 Advanced starts with units and accuracy, revises the areas of composite shapes, quadrilaterals and circles, then finds the surface areas of prisms and cylinders and the volumes of prisms, cylinders, pyramids and cones, often in practical settings such as tanks, sheds and pools.
The ten subtopics below cover metric units and accuracy, areas of composite shapes, quadrilaterals and circles, surface areas of prisms and cylinders, and volumes of prisms, cylinders, pyramids and cones. Surface Area and Volume is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Measurement and Space strand. It covers NESA outcomes MA5‑MAG‑C‑01, MA5‑ARE‑C‑01, MA5‑VOL‑C‑01 and MA5‑VOL‑P‑01, and revises the Stage 4 outcomes MA4‑LEN‑C‑01 and MA4‑ARE‑C‑01. It leads on to the surface areas of pyramids, cones and spheres.
Subtopics
Surface Area and Volume: common questions
What is the surface area of a cylinder?
A closed cylinder has two circular ends and a curved surface that unrolls into a rectangle, so \(A = 2\pi r^2 + 2\pi rh\). With diameter 8 cm and height 5 cm, \(A = 32\pi + 40\pi = 72\pi \approx 226.19\ \text{cm}^2\).
How do you work out a prism's volume?
Multiply the area of the cross-section by the length: \(V = Ah\). A prism 12 cm long whose cross-section is a trapezium with parallel sides 5 cm and 9 cm and height 4 cm has \(V = 28 \times 12 = 336\ \text{cm}^3\).
How is the volume of a cone related to a cylinder?
A cone holds one-third of a cylinder with the same base and height: \(V = \frac{1}{3}\pi r^2h\). So a cone 24 cm tall has the same volume as a cylinder of the same radius that is only 8 cm tall.
What is the difference between absolute error and percentage error?
Absolute error is half the smallest unit of the instrument. Percentage error compares it with the measurement: \(\frac{\text{absolute error}}{\text{measurement}} \times 100\%\). A length of 20 m to the nearest metre has an absolute error of 0.5 m and a percentage error of 2.5%.
Which NESA outcomes cover this topic?
Units and accuracy are MA5‑MAG‑C‑01, surface areas of prisms and cylinders are MA5‑ARE‑C‑01, and volumes of prisms and cylinders are MA5‑VOL‑C‑01 (Stage 5 Core). Pyramids and cones use the Path outcome MA5‑VOL‑P‑01, and the area and circle work revises MA4‑LEN‑C‑01 and MA4‑ARE‑C‑01.