Question

An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster?

Answer 1

So we know that the volume of a pyramid is (1/3)LWH. We are given the height of 4 inches, but we don't know the length and width immediately. What we do know is that the area of the square base of the pyramid is 3 inches. In order to find the area of a square, you simply multiply the side lengths together, which would be s*s, or s^2. So set 3 in = s^2. You find that s = \[\sqrt{3}\]
Knowing this, we find our length and width simultaneously, and we have the height too. All we have to do is plug in the values to return the volume of each pyramid. Because each pyramid will take up the same amount of space, simply divide the volume of the block by the volume of the pyramid, and you will find out how many pyramids can be made from said block. Remember to ALWAYS round down your answer if you get a decimal answer, as you are not allowed to make a portion of a pyramid, only complete pyramids.