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.
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