A union of three solids (a cylinder of diameter 20 units, a cuboid of side 20 units, and a triangular prism with base of the triangle 20 units and height 20 units) is shown below. Visualize the new solid formed by the intersection of these three solids in this arrangement. How many surfaces will the resultant solid have?
Show Hint
When counting surfaces of solids formed by intersections, consider the type of faces (flat or curved) contributed by each solid and how they overlap.
Step 1: Understanding the solids.
We are given a cylinder, a cuboid, and a triangular prism. The intersection of these three solids will create a new solid, and we need to find how many surfaces it will have.
Step 2: Visualizing the intersection.
The intersection of these solids will be influenced by the dimensions of each solid:
- The cylinder has a circular cross-section, so it will create curved surfaces in the intersection.
- The cuboid has rectangular surfaces, contributing flat faces to the intersection.
- The triangular prism has triangular faces that intersect with the other solids.
The surfaces of the resultant solid will depend on the specific way these solids overlap.
Step 3: Counting the surfaces.
- The cylinder will contribute some curved surfaces.
- The cuboid contributes rectangular faces at the edges of the intersection.
- The triangular prism contributes triangular faces.
Given the arrangement, the new solid formed will have:
- 6 rectangular surfaces (from the cuboid).
- 2 curved surfaces (from the cylinder).
- 2 triangular faces (from the triangular prism).
Thus, the total number of surfaces in the resultant solid is \( 6 + 2 + 2 = 10 \).
\[
\boxed{10}
\]
