GATE 2025 ME – Question 34

Casting, Forming and Joining Processes · Casting: patterns, moulds, cores, solidification, riser and gating design, defects · 1 mark · Numerical answer

A liquid metal is poured in a mold cavity of size 200 mm $\times$ 200 mm $\times$ 200 mm. The cooling is uniform in all directions with NO additional compensation for shrinkage. Considering the volumetric shrinkage during solidification and solid contraction as 7% and 8%, respectively, the length of the cube edge after cooling down to the room temperature is _______ mm (rounded off to 1 decimal place).

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Correct answer: 188.95 to 190.85

Explanation

The volume after solidification is $(1 - 0.07)$ of the cavity volume, and after solid contraction it is a further $(1 - 0.08)$. The volume is $200^3 \times 0.93 \times 0.92$, so the edge is $200 \times (0.93 \times 0.92)^{1/3} = 200 \times 0.9496 = 189.9$ mm.