GCSE Maths: Area, Perimeter and Volume

Area and volume questions appear on GCSE Mathematics papers at both Foundation and Higher tier, often as the first step of a longer problem. This material trains the mensuration content of the GCSE subject content for England: the areas of triangles, parallelograms and trapezia, the circumference and area of a circle, arc lengths and sector areas, and the surface area and volume of prisms, cylinders, pyramids, cones and spheres, together with the unit conversions that trip up many students.

The quiz has fourteen calculation questions. Each one gives every length you need in words, and most come with a diagram, as on the exam paper; picture the shape yourself first, then check it against the drawing. The wrong options are built from the mistakes examiners see most often: using the diameter where the radius is needed, forgetting the one third in the volume of a cone or pyramid, leaving out the half in the area of a triangle, counting an inside edge in the perimeter of a compound shape, and converting square or cubic units with the wrong factor. Several questions ask for an exact answer in terms of $\pi$, others for a decimal rounded to a given accuracy, because both forms are expected at GCSE.

The flashcards collect the formulae and the vocabulary in one place: the area of a trapezium, arc length and sector area as fractions of the whole circle, the volume of a prism as cross-section times length, the cone formulae with the slant height from Pythagoras' theorem, the sphere formulae, and the link between cubic centimetres and litres. Some of these formulae must be learnt by heart, while others, such as the sphere and cone formulae, are given in the question when they are needed, so use the cards to know which is which.

The printable written work has eight longer problems to answer by hand: a trapezium and a triangle of equal area, a full circle and a sector, a cylinder and a cone with total surface areas, a composite solid made from a cylinder and a hemisphere, a water tank measured in metres and litres, and a reverse problem where you find the radius of a sphere from its volume. Each problem asks you to show the method, not only the final number, which is how marks are awarded in the exam.

Use the quiz to check that you choose the right formula quickly, then use the written work to practise setting out a full solution with units. The material suits Year 10 and Year 11 students on either tier; arc and sector questions and the cone and sphere problems are a good test of whether you are ready for the harder questions on a paper.

• Calculate the areas of triangles, parallelograms, trapezia and compound shapes
• Find the circumference and area of a circle, exactly in terms of pi or rounded
• Calculate arc lengths, sector areas and sector perimeters
• Find the volume and surface area of prisms, cylinders, pyramids, cones and spheres
• Use Pythagoras' theorem to find the slant height of a cone
• Convert between units of area, volume and capacity

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Geometry and measures: mensuration and calculation (G14, G16, G17, G18).