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This lesson covers the volume and surface area of 3D shapes for AQA GCSE Mathematics. You need to know the formulae for cuboids, prisms, cylinders, pyramids, cones and spheres. Higher-tier students must also handle frustums and compound solids. These topics are heavily tested and carry significant marks on the exam.
Volume is the amount of 3D space a solid occupies. It is measured in cubic units (e.g. cm cubed, m cubed).
Volume = length x width x height
A cuboid has dimensions 5 cm by 4 cm by 3 cm. Find its volume.
Solution: Volume = 5 x 4 x 3 = 60 cm cubed
A prism is any 3D shape with a uniform cross-section.
Volume of a prism = area of cross-section x length
A triangular prism has a cross-section that is a right-angled triangle with base 6 cm and height 4 cm. The prism is 10 cm long. Find its volume.
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