Consider the Region in 3-Space Bounded by the Surface $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 1$

Essay

Consider the region in 3-space bounded by the surface $f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 1$ and the plane $z = k$ where $k > 0$ .Find the value of k such that the volume of this region below the xy-plane equals the volume of this region above the xy-plane.