Cuboids, Rectangular Prisms and Cubes
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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. |
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Volume and Surface Area
The volume is found using the formula:
Volume = Height × Width × Length
Which is usually shortened to:
V = h × w × l
Or more simply:
V = hwl
Surface Area
And the surface area is found using the formula:
A = 2wl + 2lh + 2hw
Example: Find the volume and surface area of this cuboid.
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V = 4×5×10 = 200
A = 2×4×5 + 2×5×10 + 2×10×4
= 40+100+80 = 220 |
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Square Prism
When at least two of the lengths are equal it can also be called a square prism.
(Note: this doesn't stop it from also being called a rectangular prism if you want!) |
Cube
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. |
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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).
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!
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| A box with a slot cut as a handle |
Cuboids in a cuboid room |
Boxes for model trains |
Now that's just silly! |
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