Question

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. The height of the scale model is 9 inches less than its length and its base is a square. If the volume of the model is 6300 cubic inches, write an equation describing the situation.

Answer 1

Answer:

The equation that describe the situation is

$b^{3}-9b^{2}-18,900=0$

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

$V=\frac{1}{3}b^{2} h$

where

b is the length side of the square

h is the height of the pyramid

we have

$V=6,300\ in^{3}$

$h=(b-9)\ in$

substitute the values and solve for b

$6,300=\frac{1}{3}b^{2} (b-9)\\ \\18,900=[b^{3}-9b^{2}]\\ \\b^{3}-9b^{2}-18,900=0$

Using a graphing calculator

$b=30\ in$

$h=(30-9)=21\ in$