VOLUME OF RECTANGULAR PRISMS

Prism is basically a 3D shape. Even though we have different formulas to find volume of different kinds of prisms, the basic idea of finding volume is to multiply the base area and height of the prism.

A rectangular prism has six faces. Any pair of opposite faces can be called the bases of the prism. All the side walls are either rectangles or squares (that is, no side wall is triangle), then prism will look like as given below. 

Volume of a rectangular prism is

= l x w x h

or

= Base Area x Height

Find the volume of the rectangular prism :

Example 1 :

Solution :

We can find volume of the rectangular prism (cuboid) using the formula given below.

Base area x Height

Here, the base is a rectangle with length 12 cm and width 4 cm.

Area of the base is

= 12 x 4

= 48 cm²

Height of the cuboid is 8 cm.

So, volume of the above cuboid is

= 48 x 8

= 384 cm³

Example 2 :

Solution :

We can find volume of the rectangular prism using the formula given below.

Base area x Height

Here, the base is a rectangle with length 3 m and width 2 1/4 m.

Area of the base is

= 3 x 2 1/4

= 3 x 9/4

= 27/4 m²

Height of the rectangular prism is 4 1/2 m.

So, volume of the above rectangular prism is

= 4 1/2  x 27/4

= (9/2)  x (27/4)

= 243/8

= 30 3/8 m³

Example 3 :

Solution :

We can find volume of the rectangular prism using the formula given below.

Base area x Height

Here, the base is a rectangle with length 7 1/2 inches and width 4 inches.

Area of the base is

= 7 1/2 x 4

= (15/2) x 4

= 30 in²

Height of the rectangular prism is 2 1/2 inches.

So, volume of the above rectangular prism is 

= 30 x 2 1/2

= 30  x 5/2

= 150/2

= 75 in³

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