Question 1099545
The volume of the pyramid is V = (1/3)Bh.  The area of the base, B is equal to x^2.
And since the height is 9 cm less than the length of the sides, h = x - 9
Therefore V in terms of x is:
a) V(x) = (1/3)x^2*(x-9)
b) (1/3)x^2*(x-9) = (1/3)x^3 - 3x^2 = 6300
Multiply through by 3:
x^3 - 9x^2 - 18900 = 0
c) We need to show that the length of the base, x = 30 cm
That implies that x - 30 must be a factor.
Dividing x^3 - 9x^2 - 18900 by x - 30 gives x^2 + 21x + 630, which cannot be factored any further
The factorization is (x-30)(x^2 + 21x + 630)
d) For the scale model h = x - 9 -> h = 30 - 9 = 21
If all dimensions are scaled up by the factor 250/4, the new height will be 250/4*21 = 1312.5 cm