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Cuboids, Rectangular Prisms and Cubes

A cuboid is a box-shaped object. It has six flat sides and all angles are right angles.

And all of its faces are rectangles.

It is also a prism because it has the same cross-section along a length. In fact it is a rectangular prism.

If at least two of the lengths are equal then it can also be called a square prism.

(Note that this doesn't stop it from also being called a rectangular prism if you want!)

If all three lengths are equal it can be called a cube (or hexahedron) and each face will be a square.

A cube is still a prism.

And a cube is one of the Platonic Solids.

So a cube is just a special case of a square prism, and
a square prism is just a special case of a rectangular prism.
And they are all cuboids

Note: The name "cuboid" comes from "cube" and -oid (which means "similar to, or resembling") and so indicates "it is like a cube".

Another use of -oid is when we talk about the Earth being a spheroid (not exactly a sphere, but close).

Volume and Surface Area

The volume of a cuboid is simply: Volume = width × depth × height
Which can be written as: V = wdh
And the surface area is: A = 2wd + 2dh + 2hw

Example Calculation



Find the volume and surface area of this cuboid.

V = 4×5×10 = 200

A = 2×4×5 + 2×5×10 + 2×10×4
    = 40+100+80 = 220

Examples of Cuboids

Cuboids are very common in our world, from boxes to buildings we see them everywhere. You can even fit them inside other cuboids!

A box with a slot cut as a handle Cuboids in a cuboid room Boxes for model trains Now that's just silly!