VOLUME OF RECTANGULAR PRISMS

Volume of rectangular prisms (Cuboid) :

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

Volume of rectangular prisms - Examples

Problem 1 :

Find the volume of the cuboid given below.

Solution :

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

Volume of the cuboid   =  Base area x Height

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

Area of base  =  12 x 4  =  48 sq. cm

Height of the cuboid  =  8 cm

Volume of cuboid   =  48 x 8

Volume of cuboid   =  384 cubic cm

Problem 2 :

Find the volume of the rectangular prism given below.

Solution :

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

Volume of the rectangular-prism is

=  Base area x Height

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

Area of base  =  3 x 2 1/4  =  3 x 9/4  =  27/4 sq.m

Height of the rectangular-prism  =  4 1/2 m

Volume of rectangular-prism  =  4 1/2  x 27/4

Volume of rectangular-prism  =  (9/2)  x (27/4)

Volume of rectangular-prism  =  243/8

Volume of rectangular-prism = 30 3/8 cubic meters

Problem 3 :

Find the volume of the rectangular prism given below.

Solution :

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

Volume of the rectangular-prism is

=  Base area x Height

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

Area of base  =  7 1/2 x 4  =  (15/2) x 4  =  30 sq.inches.

Height of the rectangular prism  =  2 1/2 inches

Volume of rectangular-prism  =  30 x 2 1/2

Volume of rectangular-prism  =  30  x 5/2

Volume of rectangular-prism  =  150/2

Volume of rectangular-prism  =  75 cubic inches

After having gone through the stuff given above, we hope that the students would have understood "Volume of rectangular-prisms".

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