Question

Shown below is the front and top views of two cubes. The red and blue cubes are made up of metal and wax respectively. Red cube is heated and is hot enough to melt wax in the blue cube. As shown in the front and top views, the red cube is moved along the path PQRS creating sharp edges and flat surfaces on the blue cube. What is the total number of surfaces the blue cube will have after the red cube reaches the point S?

Hint:

When analyzing shapes that change during a process (like a cube being modified by another object), consider how many faces are being exposed or altered during each step. In this case, the movement of the red cube alters the surfaces of the blue cube.

Answer 1

Correct Answer: 16

Step 1: Analyze the given information.
The red cube is moving along the path PQRS, creating sharp edges and flat surfaces on the blue cube as it moves. Initially, the blue cube has 6 surfaces (as it is a cube). Each time the red cube moves along a different part of the blue cube, it modifies the surfaces, either by flattening or exposing new surfaces.
Step 2: Analyze the effect of the red cube movement.
As the red cube moves, it will melt the wax on the blue cube and expose more surfaces of the blue cube. The movement will expose additional surfaces along the path PQRS. This leads to the creation of 16 total surfaces on the blue cube.
Step 3: Conclusion.
Thus, the total number of surfaces the blue cube will have after the red cube reaches point S is \( \boxed16 \).