Question
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?
Options :
a/3
a/2
a/4
a/6
Answer :
a/2
Solution :
ts ∝ V/A
cube of edge length = a
Volume and area of cube: V = a3, A = 6a2
cylindrical riser with height = h , radius = r
Volume and area of riser: V = πr2h , A = 2πrh
(ts)Riser ≥ (ts)casting
r ≥ a/3
r = a/3
from optionsr = a/2 also satisfies.
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