Mechanical Engineering > GATE 2025 > Casting
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is ______ (rounded off to 2 decimal places). Assume that solidification time follows Chvorinov's rule with an exponent of 2.
Correct : 0.85
The answer given is 1.24, but please verify with the official GATE 2025 answer key as this is a calculation-heavy problem.
By Chvorinov''s rule, solidification time t ∝ (V/SA)2, so the ratio is:
tcube / tcyl = (Mcube / Mcyl)2
For a cube of side a: Mcube = a/6 = V1/3/6.
For a cylinder where diameter = height (d = h): Volume = πd3/4, Surface Area = 3πd2/2, so Mcyl = d/6 = (4V/π)1/3/6.
Ratio Mcube/Mcyl = (π/4)1/3 ≈ 0.923 → t ratio = (0.923)2 ≈ 0.85.
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