Question

Four objects that are symmetrical along vertical planes are placed in four containers in the orientation shown below. Molten wax is poured in each of these containers up to the level indicated on the objects. Assuming that wax does not stick to the objects, which of the objects will leave its exact negative impression on the set wax when they are vertically lifted?

• A. Fig A
• B. Fig B
• C. Fig C
• D. Fig D

Hint:

A horizontal cylinder submerged exactly to its center forms a draft-neutral semi-cylinder that is always moldable. However, if submerged even slightly above its center, it immediately creates an undercut.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question tests your understanding of draft angles, moldability, and "undercuts" in product design and casting. We must determine which of the submerged 3D shapes can be extracted vertically upward from solidified wax without tearing or locking against the rigid wax cavity.

Step 2: Key Formula or Approach:
For a clean vertical release from a solid mold:

• The cross-sectional area of the submerged portion must be monotonically non-decreasing as we move upward toward the parting line (the yellow dashed wax level).

• Any horizontal expansion below the liquid level creates a mechanical lock (an undercut).

• Mathematically, the surface normal vector \(\hat{n}\) pointing outward from any submerged surface must have a non-negative vertical component (\(n_z \ge 0\)).


Step 3: Detailed Explanation:

• Let us analyze

Object A:
- It features a central rectangular housing with vertical side walls (\(n_z = 0\)) and a horizontal cylinder projecting to the right.
- The yellow wax level aligns precisely with the horizontal diameter (the widest plane) of this cylinder.
- Below this midline, the cylindrical surface curves inward toward the bottom. When lifted upward, every point on the cylinder instantly moves away from the wax cavity walls. Since there are no overhanging walls below the wax line, Object A releases perfectly.

• Let us analyze

Object B:
- This geometry consists of two mutually perpendicular horizontal cylinders intersecting one another.
- The wax level is set exactly at the horizontal midlines of both cylinders.
- Because the submerged cavity is entirely composed of semi-cylindrical troughs that taper inward toward the base, there are zero undercuts. Object B releases perfectly.

• Let us analyze

Object C:
- The main body has outward-sloping wedge walls that expand as they travel downward toward the bottom of the container.
- Because the base of the object is wider than its cross-section at the yellow wax line, the solid wax formed above the wide base acts as a physical barrier. Attempting to lift it will shatter the wax. Therefore, Object C fails.

• Let us analyze

Object D:
- This object incorporates an open architectural archway (a through-hole tunnel) running through its base.
- The liquid wax flows completely through this tunnel since the wax level is above the arch. Once solidified, a solid bar of wax passes right through the object, locking it permanently in place. Therefore, Object D fails.


Step 4: Final Answer:
Objects (A) and (B) will leave their exact negative impressions upon vertical lifting.