Your equations for the volumes are both correct.
I assume you can use this site or Desmos or something to make the graphs.
From the graph you'll see the two volume functions intersect at the point (8,448)
Let's show this algebraically.
\(x^2(x-1) - 7x^2=0\\ \forall x \neq 0\\ x-1-7 = 0\\ x-8=0\\ x=8\)
The wax cost funtion is just the volume functions times $0.01, provided x is given in cm.
Brick is cheaper to make than Egypt up to a base width of 8cm. At that size both candles cost $4.48.
Larger than that the Egypt becomes cheaper to make.