Volume of a Rectangular Prism
Related Pages
Volume Formulas
Volume Of Pyramids
Explanations For The Surface Area Formulas
More Geometry Lessons
Solid geometry is concerned with three-dimensional shapes.
In this lesson, we will learn
- how to find the volume of a rectangular prism.
- how to solve word problems about rectangular prisms.
Volume of a Rectangular Prism
A rectangular prism is a 3-dimensional object with six rectangular faces. All its angles are right angles and opposite faces are equal.
In a rectangular prism, the length, width and height may be of different lengths. A rectangular prism is also called a cuboid or rectangular solid. A cube is a special case of a cuboid in which all six faces are squares.
Formula for the Volume of a Rectangular Prism
The following diagram shows the formula to find the volume of a rectangular prism. Scroll down the page for more examples and solutions on how to find the volume of a rectangular prism.
Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets
The volume of the above rectangular prism would be the product of the length, width and height that is
Volume of rectangular prism = length × width × height
V = lwh
Surface area of rectangular prism = 2(lw + wh + lh)
Worksheet to calculate the volume and surface area of a rectangular prism.
Example:
Find the volume of the following rectangular prism or cuboid.
Solution:
Volume = l × w × h
= 6 cm × 3 cm × 4 cm
= 72 cm3
Videos
Reviews the concept of volume and uses a rectangular prism as an example
Imagine filling the prism with unit cubes (e.g., 1 cm by 1 cm by 1 cm cubes).
The length tells you how many unit cubes fit along one dimension of the base.
The width tells you how many unit cubes fit along the other dimension of the base.
Multiplying length × width gives you the area of the base, or how many unit cubes fit in one layer on the bottom.
The height tells you how many such layers of unit cubes can be stacked on top of each other.
Therefore, multiplying length × width × height gives you the total number of unit cubes that can fit inside the prism, which is its volume.
How to find the volume of two rectangular prisms?
Word problems about rectangular prisms
The following video shows how to solve a word problem involving a rectangular prism.
Example:
An exotic fish is placed in a rectangular aquarium that has a length of 75 cm and a width of 35 cm.
If the water level rises 2 cm when the fish is placed in the aquarium, what is the volume of the fish?
Volume and Surface Area of a Rectangular Solid
How to solve problems for volume of a rectangular prism?
Example:
If 1 cubic centimetre = 1 ml of water, how much water can fit in this fish tank?
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