From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Surface Area and Volume

Surface Area and Volume

At a Glance - Volume of Pyramids

Although we might wonder how much tinfoil it takes to cover the Egyptian pyramids, finding out how many mummies fit inside it would be much more interesting. Provided they don't form an undead army and attack you, that is.

If we have a pyramid with the same base (B) and height (h) as a prism, we can try and deduce its volume. The empty space in front and back of the pyramid can form another pyramid, and same with the empty space on either side of the pyramid. As it turns out, the prism can hold the volume of exactly three pyramids. Trippy, right?

If you have trust issues with us, fill these prisms and pyramids with sand or water or something and see for yourself. We don't lie (that much). You should end up with this formula for the volume of a pyramid.

Using this formula, we can calculate how much space we have inside the Egyptian pyramids.

Sample Problem

If an Egyptian pyramid has a square base with an edge length of 700 feet and a height of 450 feet, what's the pyramid's volume?

V = ⅓(700 ft)2(450)

Drumroll, please.

V = 73,500,000 ft3

Or seven times as much in cubic dog-feet.

Example 1

Find the volume of the square pyramid.



Example 2

Find the volume of this regular (but not right) pentagonal pyramid.


Exercise 1

Find the volume of the rectangular pyramid.


Exercise 2

Find the volume of the triangular pyramid. 


Exercise 3

We're vacationing in Egypt and we come across the Pyramid of Giza. Its square base has an edge of 756 feet and it's 453 feet high. If it were filled to the brim with nothing but mummies, how creepy would that be? Answer: A lot. How many mummies would it hold? Assume a mummy takes up about 12 cubic feet of space.


People who Shmooped this also Shmooped...

Advertisement