Word problem for algebra about volume

Question

The volume of one of the buildings in the downtown area is 235,224 cubic meters. The building is 9 times as tall as the radio tower on top of the building. The square base has a side that is 22 times 3 meters less the height of the radio tower. What is the dimensions of the building? How tall is the radio tower?

Answer 1

Let, height of the tower = h m

 

side of the square base = 22*(h-3) m

 

height of the building = 9*h m

 

Therefore,

 

{22*(h-3)}²*9*h=235224

 

=> 9*h³-54*h²+81*h-486=0

=>(h-6)*(9*h²+81)=0

=> h=6; as (9*h²+81) cannot be zero.

 

So, radio tower is 6 m tall.

 

building is 54 m tall and side of the square base is 66 m.