Polynomials word problems

Question

A pyramid and a cube monument are being created for a display. Their volumes are supposed to be the same. The volume of a pyramid is ⅓ times the height times the base area (V=13hb). The pyramids height (h) and base area (b) are given: h=(3x+6) and b=x2+2x+1. The volume of the cube is V=x3+4x2+27. What value of x would make the volumes the same? What is the volume of the cube? 

Answer 1

Given height (h) and base (b) of the pyramid:

h=3x+6

b=x²+2x+1

Given volume of a cube:

V = x³+4x²+27

Their volumes are supposed to be the same:

(1/3)•b•h = V

(1/3)(x²+2x+1)(3x+6) = x³+4x²+27

(x²+2x+1)(x+2) = x³+4x²+27

x³+4x²+5x+2 = x³+4x²+27

5x+2 = 27

5x = 25

x = 5

V = (5)³+4(5)²+27

V = 125 +100 +27

V = 252 cubic unit.