# Question Video: Finding the Height of a Pyramid in a Real-World Context

The Louvre Pyramid in Paris has a square base whose sides are 112 feet long. Given its volume is 296875 cubic feet, find the height of the pyramid to the nearest foot.

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### Video Transcript

The Louvre Pyramid in Paris has a square base whose sides are 112 feet long. Given its volume is 296875 cubic feet, find the height of the pyramid to the nearest foot.

In this question, we’re given that there is a pyramid which has a square base, and these lengths of the square are 112 feet. We’re given the volume, but we need to calculate the height of this pyramid. We can remember that to find the volume of a pyramid, we calculate one-third times the area of the base times the perpendicular height. Here, we have got the volume of the pyramid. We need to calculate the perpendicular height. We don’t know the area of the base, but we can calculate this.

The area of a square is the length squared. So, in this case, we need to calculate 112 squared. This gives us 12544, and the units will be square feet. Now, we can apply the volume formula, filling in the given value 296875 as the volume and the area of the base that we’ve just calculated as 12544. Because we wish to find the value of ℎ, when we rearrange this, we can begin by multiplying both sides by three. Next, we can divide both sides by 12544. This gives 71.00 and so on is equal to ℎ. As we’re asked to give the value to the nearest foot, we can write the answer so that we find the height of the Louvre Pyramid as 71 feet.