If the ends of a solid (i.e. a three-dimensional object) are not regular polygon but have identical cross-sections when cut by a plane parallel to
one of the ends, then the solid is said to be an **irregular prism**.
## Volume of a Prism
In this section, we will consider the volume of a cube, cuboid, cylinder and triangular prism.
If the rectangular box were filled with 1 cm cubes, there would be:
As there are 3 layers,
Now note that the area of the box's base is given by:
From the above discussion, we can derive a formula for the volume of a** **rectangular box as follows:
In general:
The volume, *V*, of a prism is given by
**
**
where *A* is the area of the base (or cross-section) of the prism
and *h* is the height.
The volume of the following solids are often required to solve real
world problems involving quantity, capacity, mass and strength of
materials including liquids.
A cube of side-length *l* units has a volume of *V* cubic
units given by
A cuboid with length *l* units, width *w* units and height *h* units has a volume of *V* cubic units given by
A cylinder with radius *r *units and height *h* units has a
volume of *V* cubic units given by
A triangular prism whose length is *l* units, and whose triangular
cross-section has base *b* units and height *h* units, has a
volume of *V* cubic units given by
Example 2
Find the volume of a cube of side 5 cm. |