VOLUME OF PRISM

Volume of prism :

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.

When we are trying to find volume of a prism, we have to consider the following important points.

1. Let the base of a prism be a rectangle or square. If all the side walls are either rectangles or squares (that is, no side wall is triangle), then prism will look like as given below.

The formula to find volume of the above prism

=  Base area x Height

2. Let the base of a prism be a rectangle or square. If two of the side walls side walls are triangles and other two side walls are rectangles or squares, then prism will look like as given below.

The formula to find volume of the above prism

=  (1/2) x Base area x Height

3. Let the base of a prism be a triangle. If all of the side walls are rectangles or squares, then the prism will look like as given below.

The formula to find volume of the above prism

=  Base area x Height

4. Let the base of a prism be a rectangle or square or triangle. If all of the side walls are triangles, then the prism will be a pyramid and it will look like as given below.

The formula to find volume of the above pyramid

=  (1/3) x Base area x Height

Volume of prism - Practice problems

Problem 1 :

Find the volume of the cuboid given below.

Solution :

Here, the base is  a rectangle and all the side walls are also rectangles.

Then, we have

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

Let us look at the next problem on "Volume of prism"

Problem 2 :

Find the volume of the cube given below.

Solution :

Here, the base is  a square and all the side walls are also squares.

Then, we have

Volume of the cube   =  Base area x Height

Here, the base is a square with side length of 8 cm.

Area of base  =  8 x 8  =  64 sq. cm

Height of the cube  =  8 cm

Volume of cube  =  64 x 8

Volume of cuboid   =  512 cubic cm

Let us look at the next problem on "Volume of prism"

Problem 3 :

Find the volume of the triangular prism given below.

Solution :

Here, the base is  a rectangle, two of the side walls are triangles and other two side walls are rectangles.

Then, we have

Volume of the prism   =  (1/2) x Base area x Height

Here, the base is a rectangle with length 7 cm and width is 4 cm.

So, area of the base  =  7 x 4  =  28  sq. cm

Height of the prism  =  3 cm

Volume of the prism  =  (1/2) x 28 x 3

Volume of the prism  =  42 cubic cm

Let us look at the next problem on "Volume of prism"

Problem 4 :

Find the volume of the triangular prism given below.

Solution :

Here, the base is  a rectangle, two of the side walls are triangles and other two side walls are rectangles.

Then, we have

Volume of the prism   =  (1/2) x Base area x Height

Here, the base is a rectangle with length 12 cm and width is 8 cm.

So, area of the base  =  12 x 8  =  96 sq. cm

Height of the prism  =  3 cm

Volume of the prism  =  (1/2) x 96 x 3

Volume of the prism  =  144 cubic cm

Let us look at the next problem on "Volume of prism"

Problem 5 :

Find the volume of the triangular prism given below.

Solution :

Here, the base is  a triangle, and all the side walls are rectangles.

Then, we have

Volume of the prism   =  Base area x Height

Here, the base is a triangle with base 6 cm and height 4 cm.

So, area of the base  =  (1/2) x 6 x 4  =  12 sq. cm

Height of the prism  =  8 cm

Volume of the prism  =  12 x 8

Volume of the prism  =  96 cubic cm

Let us look at the next problem on "Volume of prism"

Problem 6 :

Find the volume of the pyramid given below.

Solution :

Volume of the pyramid   =  (1/3) x Base area x Height

Here, the base is a square with side length 8 cm.

So, area of the base  =  8 x 8  =  64 sq. cm

Height of the pyramid  =  9 cm

Volume of the pyramid  =  (1/3) x 64 x 9

Volume of the prism  =  192 cubic cm

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

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