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Surface Area and Volume

Surface Area and Volume

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.

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