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.
