Project ForgeThe solidification time of a casting is proportional to (V/A)², where V is the volume of the casting and A is the total casting surface area losing heat. Two identical cubes of same material and size are cast using a sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is
- A25/36
- 36/25
- C1
- D6/5
Explanation
For a cube of side a: normal cube loses heat from all 6 faces, A=6a², so t1∝(a/6)²=a²/36. With the top face insulated, only 5 faces lose heat, A'=5a², so t2∝(a/5)²=a²/25. Ratio t2/t1 = (a²/25)/(a²/36) = 36/25.
Source: GATE ME 2015 (Session 1) (2015)
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