The Louvre Pyramid is a tourist attraction in Europe. It is a square pyramid, with a height of 21m, and base of side length 35m. The four faces of this pyramid are covered in glass, of thickness 0.03m. Find the volume of glass used to construct the exterior of the Louvre.

Emmanuel Pace

Emmanuel Pace

Answered question

2022-07-22

Using Differentials to Calculate the Volume of a Square Pyramid
Use differentials to solve the problem:
The Louvre Pyramid is a tourist attraction in Europe. It is a square pyramid, with a height of 21m, and base of side length 35m. The four faces of this pyramid are covered in glass, of thickness 0.03m. Find the volume of glass used to construct the exterior of the Louvre.
I know that the volume of a square pyramid is: V = a 2 h 3 , where a is its base length and h is its height.
I then solved for d V = a 2   d h + 2 a h   d a 3 , but I am stuck in this equation because there are many unknowns.
The next step I can think of is finding the volume, which can be in the form of: V G l a s s = V ( V a l u e + 0.03 ) V ( V a l u e ), which can be evaluated like: L ( x ) = f ( x 0 ) + f ( x 0 ) ( x x 0 ), but I am not sure of the way of finding the V(Value).

Answer & Explanation

ri1men4dp

ri1men4dp

Beginner2022-07-23Added 14 answers

Step 1
Why do you think you have many unknown in this formula ?
d V = a 2   d h + 2 a h   d a 3
You have all the information that you need to find your dV.
The only apparently unknown is d which could be found by
d h = 3 sin α
where tan α = a 2 h

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