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