A hotel in Las Vegas, Nevada, is the largest pyramid in the United States. Prior to the construction of the building, the architects designed a scale model. If the height of the scale model was 9 inches less than its length and its base is a square, write a polynomial function that describes the volume of the model in terms of its length.

Question

Luca Castro

Mathematics

2 April, 02:52

A hotel in Las Vegas, Nevada, is the largest pyramid in the United States. Prior to the construction of the building, the architects designed a scale model. If the height of the scale model was 9 inches less than its length and its base is a square, write a polynomial function that describes the volume of the model in terms of its length.

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Javion · Answer 1

The volume of a square pyramid is:

V = (1/3) LxWxH

From the problem we know that:

H = L - 9 and

W = L

Substituting this to the formula of the volume to generate a polynomial function:

V = f (L) = (1/3) L x L x (L - 9)

Expanding:

f (L) = L³/3 - 3L²