If you happen to be viewing the article Volume of Prism Formula? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
We know that geometry deals with the study of 2D shapes and 3D shapes. A polyhedron is a three-dimensional shape that is formed by polygons. The word polyhedron is made of ‘poly’ meaning many and ‘hedron’ meaning face.
Every polygon in a polyhedron is called a face. The two faces meet in a line segment that is called edge. The point of intersection of three or more edges is called a vertex.
There are two important members of the polyhedron family: Prisms and pyramids. In this article, we will be discussing what is prisms, different types of prisms, the volume of prism formula, and how to calculate the volume of a prism.
Contents
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.
(image will be uploaded soon)
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
(image will be uploaded soon)
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
(image will be uploaded soon)
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
(image will be uploaded soon)
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
(image will be uploaded soon)
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
(image will be uploaded soon)
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
(image will be uploaded soon)
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.
(image will be uploaded soon)
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.
(image will be uploaded soon)
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:
-
Find the volume for the triangular prism given below
(image will be uploaded soon)
Thank you so much for taking the time to read the article titled Volume of Prism Formula written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
