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Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the top of the casting. Assume solidification time, tₛ ∝ V/A, where V is the volume and A is the total surface area dissipating heat. If the top of the riser is insulated, which of the following radius/radii of riser is/are acceptable?

1. a/3
2. a/2
3. a/4
4. a/6

Correct answer: a/2

Solution

The correct option, a/2, is acceptable because it provides a sufficient volume-to-surface area ratio that allows for effective heat dissipation during solidification, ensuring that the riser can maintain a liquid state longer than the casting, thus feeding it as it cools.

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