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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Consider the Region in 3-Space Bounded by the Surface f(x,y)=x2+y2−1f ( x , y ) = x ^ { 2 } + y ^ { 2 } - 1f(x,y)=x2+y2−1

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