Question

A UNION of two solids, a pentagonal prism and a hexagonal prism, is shown. The side view depicts how they intersect. Visualise the new solid formed by their INTERSECTION (the part common to both). How many surfaces will the new solid have? 

Hint:

Intersection solids usually have more surfaces than either of the two prisms individually. Count faces from both prisms’ cross-sections.

Answer 1

Step 1: Understand intersection.
- A pentagonal prism has 7 surfaces (2 pentagons + 5 rectangles).
- A hexagonal prism has 8 surfaces (2 hexagons + 6 rectangles).
Step 2: Intersection shape.
When they intersect perpendicularly, the common region has cross-sections of both prisms.
- The resulting solid is bounded by flat polygonal surfaces.
- Careful visualization shows the intersection gives rise to 10 surfaces.
Final Answer: \[ \boxed{10} \]