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.

Question

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.

Reiny · Answer

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