From one side of a solid cube of side 2 units, a square pyramid of height 1 unit was removed as shown in the image, resulting in a solid with 9 surfaces. If one more pyramid of the same dimensions is removed from another side of the resultant solid, how many surfaces can the new resultant solid have?
To solve this question, we need to determine the number of surfaces of the solid when a second pyramid is removed from the cube.
Initially, we have a cube with side length of 2 units, which means:
1. The total number of surfaces of a cube is 6.
After removing the first pyramid from one side of the cube:
The pyramid has a square base with the same dimension as the cube’s face (2x2) and a height of 1 unit.
Upon removal, 4 triangular faces of the pyramid become exposed.
Thus, the original face of the cube where the pyramid was removed is replaced with these 4 triangular faces.
As a result, after the first removal, we have an additional triangular face.
This gives a total of 9 surfaces: 5 remaining cube faces + 4 triangular pyramid faces.
When the second pyramid with the same dimensions is removed from another face of the solid, consider:
The new pyramid removal exposes 4 more triangular faces on another original cube face.
One triangular face from each pyramid will meet at the edge of the cube (since cube's original edge length equals the pyramid base edge length), forming a single surface instead of two separate ones.
This results in one less surface compared to if they did not meet.
Counting all surfaces:
Originally 6 cube faces
Minus 2 cube faces where pyramids are removed = 4
Plus 8 triangular faces from two sets of removed pyramids
Minus 2 for the meeting edge surfaces = 10 total surfaces
Therefore, the resultant solid after removing the second pyramid will have 10 surfaces.
