Cuboids, Rectangular Prisms and Cubes

Go to Surface Area or Volume.

cuboid

A cuboid is a box-shaped object.

It has six flat faces 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!

cuboid building
A building
cuboid apple box
A box with a
slot as a handle
cuboid boxes
Cuboids in a
cuboid room
cuboid train boxes
Boxes for model trains
cuboid impossible
Now that's just silly!

 

cuboid

Square Prism

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

(Note: we can still call it a rectangular prism if we want!)

cube

Cube

When all three lengths are equal it is called a cube (or hexahedron)
and each face is 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 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).

Surface Area

The surface area is found using the formula:

Area = 2 × Width × Length + 2 × Length × Height + 2 × Width × Height

cuboid area 2wl 2lh and 2hw

 

Which can be shortened to:

A = 2wl + 2lh + 2hw

Example: Find the surface area of this cuboid

cuboid 10x5x4  
A = 2wl + 2lh + 2hw
   = 2×5×10 + 2×10×4 + 2×4×5
   = 100 + 80 + 40
   = 220

Volume

The volume of a cuboid is found using the formula:

Volume = Length × Width ×  Height

Which can be shortened to:

V = l × w × h

Or more simply:

V = lwh

Example: Find the volume of this cuboid

cuboid 10x5x4  
V = lwh
   = 10×5×4
   = 200