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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, $t_{s} \:\alpha\: V/A$, 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. $\dfrac{a}{3}$
  2. $\dfrac{a}{2}$
  1. $\dfrac{a}{4}$
  1. $\dfrac{a}{6}$
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