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.
Examples of Cuboids
Cuboids are very common in our world, from boxes to buildings we see them everywhere. We can even fit them inside other cuboids!
A box with a slot
cut as a handle
Cuboids in a
Boxes for model trains
Now that's just silly!
Volume and Surface Area
The volume of a cuboid is found using the formula:
Volume = Length × Width × Height
Which is usually shortened to:
V = l × w × h
Or more simply:
V = lwh
And the surface area is found using the formula:
A = 2wl + 2lh + 2hw
Example: Find the volume and surface area of this cuboid.
V = 10×5×4 = 200
A = 2×4×5 + 2×5×10 + 2×10×4
= 40+100+80 = 220
A cube is still a prism.
And a cube is one of the Platonic Solids.
- 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 says "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).