Final answer:
The edge of the original cubic container is 5 inches, which is the unique solution to the equation derived from the volume change and the height increase of the water when transferred to the taller container.
Step-by-step explanation:
To find the length of the edge of the original cubic container, we need to use the given information: the volume of water after pouring is 200 cubic inches, and the height increased by 3 inches when the water was poured into a taller container with the same base area. The volume of a cube is given by the formula V = s^3, where V is the volume, and s is the side length of the cube.
Let the side length of the cubic container be s inches. Therefore, the original volume of water is also s^3. When transferred to the taller container, this volume plus the extra water added totals 200 cubic inches, and the height of the water increases by 3 inches. This implies that:
s^3 + (s^2 × 3) = 200
Now, we solve the equation:
s^3 + 3s^2 - 200 = 0
By trial and error or other algebraic methods, we find that s = 5 inches. Thus, the edge length of the original cubic container is 5 inches. We can show that this solution is unique because it is the only positive real solution to the cubic equation above.