we know that
The volume of a square prism is equal to
[tex]V=A*H[/tex]
where
A is the area of the base of the prism
H is the height of the prism
The volume of the container is equal to the volume of the larger prism minus the volume of the smaller prism
Step 1
Find the volume of the larger prism
[tex]V=A*H[/tex]
In this case
[tex]A=B^{2}\ units^{2}[/tex]
[tex]H=h\ units[/tex]
[tex]V=B^{2}*h\ units^{3}[/tex]
Step 2
Find the volume of the smaller prism
[tex]V=A*H[/tex]
In this case
[tex]A=b^{2}\ units^{2}[/tex]
[tex]H=h\ units[/tex]
[tex]V=b^{2}*h\ units^{3}[/tex]
Step 3
Find the volume of the container
The volume of the container is equal to the volume of the larger prism minus the volume of the smaller prism
so
[tex]V=(B^{2}*h)\ units^{3}-(b^{2}*h)\ units^{3}[/tex]
Simplify
[tex]V=[B^{2}-b^{2}]*h\ units^{3}[/tex]
Difference of squares
[tex]V=[B-b]*[B+b]*h\ units^{3}[/tex]
therefore
the answer is
[tex]V=[B-b]*[B+b]*h\ units^{3}[/tex]
