Ready to unlock the secrets of pyramid volumes? This guide... Show more
Calculus 1
OverigeSign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
52
•
Dec 2, 2025
•
Calculating the Volume of a Pyramid
Precious
@lalalla_
1 / 3
Volume of Pyramids Formula
Ever wonder how to calculate the space inside a pyramid? The volume of any pyramid can be found using the formula V = ⅓Bh, where B is the area of the base and h is the height of the pyramid.
For rectangular pyramids, first find the base area using B = L × W. Then multiply by the height and divide by 3. For example, a rectangular pyramid with a 13 cm × 6 cm base and 14 cm height has a base area of 78 cm² and a volume of 364 cm³.
Square pyramids follow the same formula, but the base area is B = s² where s is the side length. A square pyramid with a 22 m × 22 m base and 35 m height has a base area of 484 m² and a volume of 5,646.6 m³.
💡 Remember that the height of a pyramid is always measured perpendicular to the base, not along the slant!
Working with these formulas becomes easier with practice. Try calculating the volume of a rectangular pyramid with base dimensions 17 ft × 32 ft and height 24 ft (answer: 4,352 ft³) or a square pyramid with 15 in sides and 19 in height (answer: 1,425 in³).
Triangular Pyramids
Triangular pyramids have triangular bases instead of rectangular or square ones. To find the base area, use the formula B = ½bh where b is the base of the triangle and h is the height of the triangle.
For example, a triangular pyramid with a base triangle measuring 13 units × 8 units and a pyramid height of 17 units has a base area of 52 square units. Applying our volume formula V = ⅓Bh, we get V = ⅓(52)(17) = 294.67 cubic units.
Practice problems show how versatile this formula is. A triangular pyramid with base dimensions of 16 ft × 5 ft and height 10 ft has a volume of 133.3 ft³. Another pyramid with a triangular base of area 112.5 yd² and height 20 yd has a volume of 750 yd³.
🔑 The key to solving any pyramid volume problem is finding the base area first, then applying the ⅓Bh formula!
When facing practice problems, first identify what you're looking for. For example, if given that a pyramid has a height of 5 inches and volume of 60 cubic inches, you can work backward to determine possible base shapes by using the formula V = ⅓Bh to find that the base area must be 36 square inches.
Pyramid Volume Applications
Understanding pyramid volumes helps you solve more complex problems. For example, when asked which solids have a volume of 40 cubic units, you'll need to apply different volume formulas for each shape and compare results.
When working with specific measurements, use the formula to find missing values. If a square pyramid has a volume of 50 cubic units and a base with sides of length 5 units , you can find the height by rearranging the formula: h = 3V/B = 3(50)/25 = 6 units.
Comparing different solids helps understand relationships between shapes. A cone and cylinder with the same radius and height have a volume ratio of 1:3. This means if a cone has volume 100π cubic feet, the cylinder would have 300π cubic feet.
👉 When identifying 3D shapes, focus on the number and types of faces. A triangular prism has 2 triangular faces and 3 rectangular faces.
Being able to visualize 3D shapes from their components is a valuable skill. For example, a solid constructed from 2 congruent triangles and 3 rectangles would be a triangular prism, not a pyramid (which would have a polygon base and triangular lateral faces).
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content: Pyramid
Most popular content in Geometry
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Calculating the Volume of a Pyramid
Precious
@lalalla_
Ready to unlock the secrets of pyramid volumes? This guide will help you master calculating the volume of different pyramids using a simple formula. You'll learn to apply this formula to rectangular, square, and triangular pyramids with real examples.
Volume of Pyramids Formula
Ever wonder how to calculate the space inside a pyramid? The volume of any pyramid can be found using the formula V = ⅓Bh, where B is the area of the base and h is the height of the pyramid.
For rectangular pyramids, first find the base area using B = L × W. Then multiply by the height and divide by 3. For example, a rectangular pyramid with a 13 cm × 6 cm base and 14 cm height has a base area of 78 cm² and a volume of 364 cm³.
Square pyramids follow the same formula, but the base area is B = s² where s is the side length. A square pyramid with a 22 m × 22 m base and 35 m height has a base area of 484 m² and a volume of 5,646.6 m³.
💡 Remember that the height of a pyramid is always measured perpendicular to the base, not along the slant!
Working with these formulas becomes easier with practice. Try calculating the volume of a rectangular pyramid with base dimensions 17 ft × 32 ft and height 24 ft (answer: 4,352 ft³) or a square pyramid with 15 in sides and 19 in height (answer: 1,425 in³).
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Triangular Pyramids
Triangular pyramids have triangular bases instead of rectangular or square ones. To find the base area, use the formula B = ½bh where b is the base of the triangle and h is the height of the triangle.
For example, a triangular pyramid with a base triangle measuring 13 units × 8 units and a pyramid height of 17 units has a base area of 52 square units. Applying our volume formula V = ⅓Bh, we get V = ⅓(52)(17) = 294.67 cubic units.
Practice problems show how versatile this formula is. A triangular pyramid with base dimensions of 16 ft × 5 ft and height 10 ft has a volume of 133.3 ft³. Another pyramid with a triangular base of area 112.5 yd² and height 20 yd has a volume of 750 yd³.
🔑 The key to solving any pyramid volume problem is finding the base area first, then applying the ⅓Bh formula!
When facing practice problems, first identify what you're looking for. For example, if given that a pyramid has a height of 5 inches and volume of 60 cubic inches, you can work backward to determine possible base shapes by using the formula V = ⅓Bh to find that the base area must be 36 square inches.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Pyramid Volume Applications
Understanding pyramid volumes helps you solve more complex problems. For example, when asked which solids have a volume of 40 cubic units, you'll need to apply different volume formulas for each shape and compare results.
When working with specific measurements, use the formula to find missing values. If a square pyramid has a volume of 50 cubic units and a base with sides of length 5 units , you can find the height by rearranging the formula: h = 3V/B = 3(50)/25 = 6 units.
Comparing different solids helps understand relationships between shapes. A cone and cylinder with the same radius and height have a volume ratio of 1:3. This means if a cone has volume 100π cubic feet, the cylinder would have 300π cubic feet.
👉 When identifying 3D shapes, focus on the number and types of faces. A triangular prism has 2 triangular faces and 3 rectangular faces.
Being able to visualize 3D shapes from their components is a valuable skill. For example, a solid constructed from 2 congruent triangles and 3 rectangles would be a triangular prism, not a pyramid (which would have a polygon base and triangular lateral faces).
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
1
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Similar Content
Pyramid Volume Calculations
Explore the essential formulas and methods for calculating the volume of pyramids. This summary covers the pyramid volume formula, example calculations, and related geometric concepts, making it a valuable resource for students studying geometry. Ideal for exam preparation and homework assistance.
MathsS3
Angle Relationships Study Guide
Just a simple note on Angle Relationships
Geometry11th
Interior and exterior angle measures
Interior and exterior angle measures practice
Algebra 19th
Most popular content: Pyramid
Most popular content in Geometry
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user