E LARGEST PYRAMID IN THE U.S. IS THE LUXUR HOTEL IN VEGAS. THE VOLUME OF THIS HOTEL IS 28,933,800 OR ABOUT 29 MILLION CUBIC FEET. THE HEIGHT OF THE PYRAMID IS 148 FEET LESS THAN THE LENGTH OF THE BUILDING. THE BASE OF THE BUILDING IS SQUARE. FIND THE DIMENSIONS OF THIS BUILDING. A. LET STATEMENT B. LABEL DIAGRAM C. FORMULA FOR THE VOLUME OF A PYRAMID D. EQUATION & SOLVE E. DIMENSIONS OF THE BUILDING.
let the height be x feet
then the length of building is x+148 feet
vol of pyramid = (1/3)base*height
= (1/3)x(x+148^2 = 28933800
You will get
x(x+148)^2 = 89,801,400
expand this and you will have one nasty equation.
It is highly unlikely that it will factor, so you are stuck with using one of the methods of solving a cubic.
If you are familiar with it, Newton's Method is very good
or you could try this webpage
http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic
A. Let's start by restating the problem in a clearer way.
The largest pyramid in the U.S. is the Luxur Hotel in Las Vegas. The volume of this hotel is 28,933,800 cubic feet. The height of the pyramid is 148 feet less than the length of the building. The base of the building is square. We need to find the dimensions of this building.
B. Let's label the diagram to help us visualize the problem.
We can label the length of the building as "L", the height of the pyramid as "H", and the base of the building as "B".
C. Now, let's recall the formula for the volume of a pyramid.
The formula for the volume of a pyramid is V = (1/3) * base area * height.
D. Let's set up an equation and solve for the dimensions of the building.
From the information given, we know the volume of the pyramid is 28,933,800 cubic feet. We also know that the height of the pyramid is 148 feet less than the length of the building (H = L - 148).
Since the base of the building is square, the base area can be calculated by squaring the length of one side (B = L^2).
Now, we can substitute these values into the volume formula:
28,933,800 = (1/3) * L^2 * (L - 148)
E. Let's solve the equation to find the dimensions of the building.
To solve this equation, we need to multiply all terms inside the parentheses by 3 to remove the fraction:
3 * 28,933,800 = L^2 * (L - 148)
After simplifying, the equation becomes:
86,801,400 = L^3 - 148L^2
Now, we can solve this equation using numerical methods, such as factoring, graphing, or using a calculator.
E. After solving the equation, we can find the dimensions of the building.
Once we have determined the value of L that satisfies the equation, we can substitute it back into the expression for H and B to find the dimensions of the building.