[Maths Class Notes] on Volume of a Prism Pdf for Exam

What is Prism?

A three-dimensional solid shape having its base and top as identical polygons and side faces as parallelograms are called a prism. 

A Prism is a Solid Object with:

• Identical base and top which are parallel to each other.

• The side faces are flat and parallelogram

• No curve sides

• And the same cross-section along with its length.

 

Different Types of Prism

A prism is a solid three-dimensional geometric figure with two similar ends and all flat sides. The prism is named after the shape of its base, hence a prism with a triangular base is called a “triangular prism”. So the different types of prisms are given their names on the basis of their cross-sectional figure formed. 

Types of Prisms are:

What is Volume of a Prism?

As the prism is a 3D solid object it has both the surface area and volume.

The volume of a 3D prism is defined as the total space occupied by that object. 

To calculate the volume of a prism, you just have to calculate the area of its base and multiply it by its height.

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Therefore Volume General Formula it is Represented as,

The volume of a three-dimensional prism is represented as cubic units. 

Here’s how to calculate the volume of a variety of prisms. 

Volume of Prism Formula

Different prisms have different volumes. So the formula to calculate the volume of different Prisms are:

A prism having its base and top as identical triangles and the lateral faces are rectangles is called a triangular prism.

A triangular prism has

• 5 faces

• 6 vertices and

• 9 edges

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Where,

a = Apothem length of a triangular prism

b = Base length of a triangular prism

h = height of a triangular prism

In a square prism, the base and top are congruent squares and the lateral faces are rectangles

A square prism has

• 6 faces

• 8 vertices and

• 12 edges

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Where

l = length of a square prism

b = Base of a square prism

h = height of a square prism

If a square prism has all of its faces as identical squares, then it is called a cube prism.

A cubic prism or a cube has

• 6 faces

• 8 vertices and

• 12 edges

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Where

a = edges of a cube prism( because l = w = h = a)

If the base and top of the prism are identical rectangles, then it is a rectangular prism or a cuboid.

A cuboid prism has

• 6 faces

• 8 vertices and

• 12 edges

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Where

l = length of a rectangular prism

b = Base of a rectangular prism

h = height of a rectangular prism

If the base and top of a prism are pentagons, then it is called a pentagonal prism. 

A pentagonal prism has

• 7 faces

• 10 vertices and

• 15 edges

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Where,

a – Apothem length of the pentagonal prism.

b – Base length of the pentagonal prism.

h – Height of the pentagonal prism

A hexagonal prism is a prism with six rectangular faces and top and base as hexagonal.

A hexagonal prism has

• 8 faces

• 12 vertices and

• 18 edges

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Where

a – Apothem length of the hexagonal prism.

b – Base length of the hexagonal prism.

h – Height of the hexagonal prism.

Solved Examples

Example 1 : Find the volume of the triangular prism given below.

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Solution: 

Given that a = Apothem length of a triangular prism = 9cm

b = Base length of a triangular prism = 12 cm

h = height of a triangular prism = 18cm

We have, Volume of triangular prism = ([frac{1}{2}]) a x b x h 

=  [frac{1}{2}] x 9 x 12 x 18 

= 972 [cm^{3}]

So the volume of the triangular prism is 972 cubic centimeter.

Example 2: Find the volume of rectangular prism given below.

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Solution:

Given that: l = length of a rectangular prism = 9cm

b = Base of a rectangular prism = 7cm

h = height of a rectangular prism = 13cm

We have, Volume of Rectangular Prism = l x b x h

                      = 9 x 7 x 13

          = 819 [cm^{3}]

Therefore the volume of rectangular prism is 819 cubic centimeters.

Quiz Time:

1. Find the volume for the triangular prism given below

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