Answer
Graph: E
Contour map: III
Work Step by Step
Graph is E
When $x=y$, the value of the graph must be 0. Moreover, when either x or y is constant and the other a variable, we will have sin functions. This means the x and y cross sections of the graph must be sin functions, as is true for Graph E.
Contour map is III
We can imagine taking horizontal cross sections. The contour lines will be around the hill like regions. Thus, it must be III.