Formula for calculating the volume of a vertical prism, prism shape

A prism is a polygon with two parallel and equal bases and parallelogram side faces.


Formula for calculating the volume of a vertical prism, prism shape

Comment:

  • The lateral faces of a prism are equal and parallel to each other.
  • The lateral faces are parallelograms.
  • The two bases of a prism are two equal polygons.

What is the formula for calculating the volume of a prism (V prism), the formula for calculating the volume of a vertical prism? Please refer to the article below.

Table of Contents

1. Volume of a vertical prism

Formula for calculating the volume of a vertical prism:

The volume of a right prism is equal to the product of the area of ​​the base multiplied by the height.

In there

  • Vis the volume of the prism (unit m3)
  • Bis the base area (unit m2)
  • his the height of the prism (unit m)

3. Classification of prisms

Regular prism

It is a vertical prism with a regular polygon base. The lateral faces of the prism are all equal rectangles. For example: a regular triangular prism, a regular quadrilateral... then we understand it as a regular prism.

Formula for calculating the volume of a vertical prism, prism shape

A regular quadrilateral base is called a regular quadrilateral prism.

Formula for calculating the volume of a vertical prism, prism shape

Triangular prism

  • A triangular prism has 5 faces, 9 edges, and 6 vertices.
  • The two bases are both triangular and parallel to each other; Each side face is a rectangle;
  • The sides are equal;
  • The height of a triangular prism is the length of one side.

For example:

Formula for calculating the volume of a vertical prism, prism shape

The triangular prism ABC.A'B'C' has:

- The bottom base is triangle ABC, the top base is triangle A'B'C';

The side faces are rectangles: AA'B'B, BB'C'C, CC'A'A;

- Edges:

  • Base edges: AB, BC, CA, A'B', B'C', C'A'
  • Sides: AA', BB', CC';

- Vertices: A, B, C, A', B', C'.

- Height is the length of one side: AA' or BB' or CC'.

Quadrilateral prism

- A quadrilateral prism has 6 faces, 12 edges, and 8 vertices.

- The two base faces are both quadrilaterals and parallel to each other. Each side face is a rectangle.

- The sides are equal.

- The height of a quadrilateral prism is the length of one side.

For example:

Formula for calculating the volume of a vertical prism, prism shape

Quadrilateral prism ABCD.A'B'C'D' has:

- The bottom base is quadrilateral ABCD, the top base is quadrilateral A'B'C'D';

The side faces are rectangles: AA'B'B, BB'C'C, CC'D'D, DD'A'A;

- Edges:

+ Base edges: AB, BC, CD, DA, A'B', B'C', C'D', D'A'

+ Side edges: AA', BB', CC', DD' are equal.

- Vertices: A, B, C, D, A', B', C', D'.

- Height is the length of one side: AA' or BB' or CC' or DD'.

Note: Rectangular prisms and cubes are also quadrilateral prisms.

Formula for calculating the volume of a vertical prism, prism shape

Right prism

If a prism has side edges perpendicular to the base, it is called a right prism.

Formula for calculating the volume of a vertical prism, prism shape


Note:

If the base is a rectangle, the vertical cylinder of the quadrilateral is called a rectangular box.

If a quadrilateral cylinder has 12 sides of length a, then its name is a cube.

Compare the right prism and the regular prism:

DEFINE: NATURE
+ A vertical prism is a prism with a side perpendicular to the base.

+ The side faces of a vertical prism are rectangular.

+ The side faces of the prism are perpendicular to the base face.

+ Height is the side

+ A regular prism is a vertical prism whose base is a regular polygon.

+ The lateral faces of a prism are all equal rectangles.

+ Height is the side

4. Example of calculating the volume of a vertical prism

Example 1: 

Given prism ABC.A'B'C' with base ABC being an equilateral triangle with side a = 2 cm and height h = 3 cm. Calculate the volume of this prism?

Formula for calculating the volume of a vertical prism, prism shape

Prize:

Because the base is an equilateral triangle with side a, the area is:

At this time, the volume of the prism is:

Example 2: 

Exercise 1: Given a vertical box with edges AB = 3a, AD = 2a, AA'= 2a. Calculate the volume of block A'.ACD'

Instruct:

Formula for calculating the volume of a vertical prism, prism shape

Because the side face ADD'A' is a rectangle, we have:

Example 3 : Given a vertical prism ABC.A'B'C' whose base is an equilateral triangle with side a√3, the angle between it and the base is 60º. Let M be the midpoint of BB'. Calculate the volume of the pyramid M.A'B'C'.

Prize:

Formula for calculating the volume of a vertical prism, prism shape

Therefore, we can infer that

We have:

Example 4: 

Given a regular quadrilateral prism ABCD.A'B'C'D' with a base edge of a and a face (DBC') with the base ABCD at an angle of 60º. Calculate the volume of prism ABCD.A'B'C'D?

Formula for calculating the volume of a vertical prism, prism shape

We have: at the center O of square ABCD.

On the other hand therefore

Infer

Also:

Example 5: 

Calculate the volume V of cube ABCD.A'B'C'D', knowing AC'=a√3

Formula for calculating the volume of a vertical prism, prism shape

Prize:

Let x be the length of the side of the cube.

Consider triangle AA'C right angled at A with:

Formula for calculating the volume of a vertical prism, prism shape

Therefore, the volume of the cube is V=a^3.

In addition to the formula for calculating the volume of a prism above, you can refer to more articles on the formula for calculating the volume of a solid of revolution , the formula for calculating the area and circumference of a circle ...

Sign up and earn $1000 a day ⋙

Leave a Comment

Worlds first AI candidate to run in general election

Worlds first AI candidate to run in general election

AI Steve is a virtual candidate created by artificial intelligence (AI) with the prototype of businessman Steve Endacott who will run in this year's general election in the Brighton Pavillion area - a coastal town in the South of England.

Will Manual Photo Editing Become Obsolete as AI Advances?

Will Manual Photo Editing Become Obsolete as AI Advances?

You've probably heard that every aspect of creativity is going to be obsolete because of AI. However, that's not entirely true. Manual photo editing isn't going away, even as AI advances, and here's why.

With the advent of AI tools, should you still compose your own music?

With the advent of AI tools, should you still compose your own music?

AI music makers claim to provide complete pre-made songs. So is it still worth it to produce songs yourself?

How to open Folder Options or File Explorer Options in Windows 10

How to open Folder Options or File Explorer Options in Windows 10

You can use File Explorer Options (also known as Folder Options) to change how files and folders behave, as well as how items are displayed on your computer. This guide will show you different ways to open Folder Options or File Explorer Options in Windows 10.

Nice Free Fire names, good FF names

Nice Free Fire names, good FF names

This is a beautiful Free Fire name, a good Free Fire name that you can name your character or name your army.

Worlds most powerful X-ray laser

Worlds most powerful X-ray laser

The Linac Coherent Light Source (LCLS), the world's most powerful X-ray laser located at the SLAC National Accelerator Laboratory in the US, will undergo a major upgrade that will increase the machine's X-ray energy by 3,000 times.

Worlds Most Expensive Space Telescope Captures Moment Two Galaxies Are About to Collide

Worlds Most Expensive Space Telescope Captures Moment Two Galaxies Are About to Collide

A stunning new image sent back from the world's most expensive space telescope, the James Webb Space Telescope, shows the moment two galaxies are about to collide.

How to adjust the spacing between bars and columns in Excel charts

How to adjust the spacing between bars and columns in Excel charts

Instead of leaving a wide gap in the Excel chart, users can adjust it to make the chart layout more beautiful. Below are instructions for adjusting the gap between bars and columns in Excel charts.

Why You Shouldnt Trust News Briefings From AI Chatbots

Why You Shouldnt Trust News Briefings From AI Chatbots

You should definitely think twice before using an AI chatbot to provide quick news summaries. A new report from the BBC finds that popular chatbots make major errors in their summaries.

What is Janitor AI? How to Register and Use JanitorAI

What is Janitor AI? How to Register and Use JanitorAI

Janitor AI, a special kind of chatbot powered by AI algorithms, is specially designed to make communication easy and intelligently answer your questions.

Collection of the latest Ninja Arena codes

Collection of the latest Ninja Arena codes

Discover the latest giftcodes of the game Ninja Arena.

Do console specs really matter?

Do console specs really matter?

In a device where you can't really upgrade anything other than the memory, do console specs really matter?

How to summarize YouTube videos using Gemini

How to summarize YouTube videos using Gemini

Google Gemini will also support you to summarize videos like YouTube video summary on Copilot. We will enable YouTube extension on Gemini to use video content summary.

Download the new Google Pixel wallpapers celebrating Hispanic Heritage Month

Download the new Google Pixel wallpapers celebrating Hispanic Heritage Month

These are Google Pixel wallpapers celebrating Hispanic Heritage month, and they're a little more abstract than what we're used to seeing from other Pixel wallpapers.

How to record short videos on Xiaomi Redmi 10

How to record short videos on Xiaomi Redmi 10

On Xiaomi Redmi 10, there is a short video recording feature so you can record videos and post them on Instagram Story or Facebook Story without having to use additional editing applications.