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:
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Identical base and top which are parallel to each other.
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The side faces are flat and parallelogram
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No curve sides
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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,
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Volume of a Prism (V) = Base Area × Length |
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
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5 faces
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6 vertices and
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9 edges
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Volume of Triangular Prism = ([frac{1}{2}]) a x b x h |
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
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6 faces
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8 vertices and
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12 edges
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Volume of a Square Prism = l x b x h |
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
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6 faces
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8 vertices and
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12 edges
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Volume of a Cube Prism = [a^{3}] |
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
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6 faces
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8 vertices and
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12 edges
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Volume of Rectangular Prism = l x b x h |
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
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7 faces
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10 vertices and
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15 edges
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Volume of Pentagonal Prism = ([frac{5}{2}]) a x b x h |
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
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8 faces
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12 vertices and
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18 edges
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Volume of Hexagonal Prism = 3 x a x b x h |
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:
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Find the volume for the triangular prism given below
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