Using Differentials to Calculate the Volume of a Square PyramidUse 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).

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Using Differentials to Calculate the Volume of a Square PyramidUse 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).

ri1men4dp · Accepted Answer

Step 1Why 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

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.

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