Answer:
The equation that describe the situation is
[tex]b^{3}-9b^{2}-18,900=0[/tex]
Step-by-step explanation:
we know that
The volume of a square pyramid is equal to
[tex]V=\frac{1}{3}b^{2} h[/tex]
where
b is the length side of the square
h is the height of the pyramid
we have
[tex]V=6,300\ in^{3}[/tex]
[tex]h=(b-9)\ in[/tex]
substitute the values and solve for b
[tex]6,300=\frac{1}{3}b^{2} (b-9)\\ \\18,900=[b^{3}-9b^{2}]\\ \\b^{3}-9b^{2}-18,900=0[/tex]
Using a graphing calculator
[tex]b=30\ in[/tex]
[tex]h=(30-9)=21\ in[/tex]
