Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 2 • Question 4

A regular prism has eight faces in total. Circle the name of the prism. [A] Square prism [B] Pentagonal prism [C] Hexagonal prism [D] Octagonal prism

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Video Transcript

A regular prism has eight faces in total. Circle the name of the prism. Is it a square prism, a pentagonal prism, a hexagonal prism, or an octagonal prism?

A prism is a three-dimensional shape which has a constant cross section. The cross section is the view of the inside of the shape when a solid is cut through. A cone, for example, is not a prism. When we cut through a cone, no matter the direction, the cross section changes each time. For example, if we cut it horizontally, we do get a circle each time. But the size of that circle changes depending on where horizontally we cut it.

A cylinder though is a prism. When we cut it horizontally, we will always get a circle of the same size. So the cross section of a cylinder is a circle. For a regular prism to have eight faces, it has to have two faces at each end which are parallel to each other. That leaves us with six remaining faces.

For this to be the case, the faces at each end must be hexagons. Hexagons have six sides. That means there will be six faces coming off of each edge of the hexagon. And the regular prism in this example is a hexagonal prism.

Using the same reasoning, we can work out exactly how many faces the other three shapes will have. A square has four sides. So there will be four faces coming off of each of these sides plus the two faces at each end. A square prism then has six faces. In fact, a square prism can be called a cube or a cuboid. A cube would have six identical faces, whereas a cuboid has three pairs of identical faces. A pentagon has five sides. So there will be five faces coming off of each of these sides plus the two faces at each end. That’s seven faces. And of course, an octagon has eight sides. So using the eight faces coming off of each side of the octagon plus the two at each end, an octagonal prism will have 10 faces.

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