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. 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!

Volume and Surface Area

The volume of a cuboid is found using the formula:

Volume = Height × Width × Length

Which is usually shortened to:

V = h × w × l

Or more simply:

V = hwl

The volume of the following solids are often required to solve real world problems involving quantity, capacity, mass and strength of materials including liquids.
Volume of a Cube Example 25 Find the volume of a cube of side 4 cm.
Solution:

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.

V = 4×5×10 = 200 A = 2×4×5 + 2×5×10 + 2×10×4 = 40+100+80 = 220