Question

The two objects on the left have a height of 1 cm and sides of 4 cm. The yellow object on the right has a total height of 5 cm. The cylindrical base of the yellow object has a diameter of 6 cm and a height of 1 cm. The two objects on the left are to be stacked on the yellow object on the right. After all the objects are stacked together, how many outer surfaces will the resulting structure have?

Hint:

When analyzing stacked structures, count visible surfaces layer by layer and include all inner and outer faces.

Answer 1

Step 1: Analyze the given structure.
- The two objects on the left are hollow cuboids with a square outer surface and a square cut-out in the center.
- Each cuboid has four vertical surfaces, one top surface, and one bottom surface. The cut-out adds four inner vertical surfaces.
- The yellow object on the right consists of a cylindrical base and a vertical pillar.
Step 2: Count the visible outer surfaces when stacked.
- The two cuboids contribute:
- \(4 \, \text{(outer vertical surfaces)} + 4 \, \text{(inner vertical surfaces)} + 1 \, \text{(top surface)} + 1 \, \text{(bottom surface)} = 10\) surfaces per cuboid.
- For two cuboids: \(10 \times 2 = 20\) surfaces.
- The yellow object contributes:
- \(1 \, \text{(cylindrical base top)} + 1 \, \text{(cylindrical base bottom)} + 1 \, \text{(pillar top)} + 2 \, \text{(pillar vertical sides)} = 5\) surfaces.
Step 3: Total visible surfaces.
Adding all contributions: \[ 20 \, \text{(from two cuboids)} + 5 \, \text{(from yellow object)} = 25 \, \text{total surfaces}. \]