Project ForgeManufacturing Engineering
Metal Casting
GATE 2007
Hard
Volume of a cube of side 'l' and volume of a sphere of radius 'r' are equal. Both the cube and the sphere are solid and of same material. They are being cast. The ratio of the solidification time of the cube to the same of the sphere is
- A(4π/6)³(r/l)⁶
- B(4π/6)(r/l)²
- C(4π/6)²(r/l)³
- (4π/6)²(r/l)⁴
Explanation
By Chvorinov's rule t∝(V/A)². For the cube, V/A=l/6; for the sphere, V/A=r/3. Ratio of times = (l/6)²/(r/3)² = l²/(4r²). Using equal volumes (l³=(4/3)πr³) to eliminate one variable and matching against the options numerically confirms option (D), (4π/6)²(r/l)⁴, reproduces this ratio exactly.
Source: GATE ME 2007 (2007)
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