Maximizing Surface Area: Open Middle Cube Problem (V1)

Drag any LARGE POINT to remove a small white cube from the main cube. Then answer the questions that follow.

Assuming we don't remove any small cubes from the LARGE CUBE, what is the total surface area of the LARGE CUBE?

Suppose we remove only one cube at a time. Which cube do we need to remove to cause the solid that remains to have the greatest possible surface area?

If we remove the cube you said in the answer above, what is this greatest possible surface area?

For an AR-friendly version of the app above, open this in GeoGebra 3D Calculator on your phone or tablet.

Quick Silent Demo in AR (0:00 - 0:28)