Chapter 4.4, Problem 26E

(a)

To determine

To write: A polynomial function that describes the volume of the model in terms of its length if the height of the scale model was 9 inches less than its length and its base is a square

Answer to Problem 26E

  $V=\frac{L^2\left(L-9\right)}{3}$

Explanation of Solution

Given information: Architecture: 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.

  

Calculation:

  

Area of pyramid is $\frac{1}{3}Bh$

B is area of base.

  $V=\frac{L^2\left(L-9\right)}{3}$

(b)

To determine

To write: An equation describing the situation if the volume of the model is 6300 cubic inches

Answer to Problem 26E

  $L^3-9L^2-18,900=0$

Explanation of Solution

Given information: Architecture: 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.

  

Calculation:

  

  $\begin{array}{l}\frac{L^2\left(L-9\right)}{3}=6300\\ \to L^2\left(L-9\right)=18,900\\ \to L^3-9L^2-18,900=0\end{array}$

(c)

To determine

The dimensions of the scale model.

Answer to Problem 26E

  $\text{Dimensions are: }30\times 30\times 21\text{ inches}$

Explanation of Solution

Given information: Architecture: 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.

  

Calculation:

  

  $L^3-9L^2-18,900=0$

By graphing you can estimate the zero to be at x = 30.

Confirming with synthetic division you get:

  $\left(x-30\right)\left(x^2+21x+630\right)$

Since the quadratic is prime, the only plausible answer is x = 30.

Therefore,

  $\text{Dimensions are: }30\times 30\times 21\text{ inches}$