Volume of a Rectangular Prism

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.

The volume of the above rectangular prism would be the product of the length, width and height that is

Volume of rectangular prism = 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

This video reviews the concept of volume and uses a rectangular prism as an example.

The following video shows 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.
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?

Use the given net to determine the surface area and volume of the rectangular solid.

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