Shown below are two perspective views of a solid object. The pipe section has three identical cuts on its surface along with three identical flanges. How many surfaces are there?
Show Hint
When counting surfaces of modified solids, remember to account for the original faces and any additional faces formed by cuts or flanges.
Step 1: Identifying the shape.
The object in question appears to be a pipe with three identical cuts and flanges. The cuts indicate that the original cylindrical shape has been modified. Additionally, the three identical flanges are protrusions from the surface of the pipe.
Step 2: Counting the surfaces.
- The cylinder has two circular faces at the ends (top and bottom).
- The surface of the cylindrical pipe is one continuous curved surface, but with the cuts, there are additional flat faces formed at each of the three cuts.
- Each of the three flanges also adds a surface.
Thus, the number of surfaces can be counted as follows:
- 2 circular faces
- 1 curved surface (which becomes subdivided into smaller flat areas due to the cuts)
- 3 flat surfaces formed by the cuts
- 3 additional flat surfaces formed by the flanges
In total, the number of surfaces is \( 2 + 1 + 3 + 3 = 9 \).
\[
\boxed{9}
\]
