GATE 2023 PI – Question 57
A cubical casting initially has side 100 mm. Volumetric solidification shrinkage and subsequent solid contraction are each 10%; shape is retained on cooling to room temperature. Find the room-temperature side in mm to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 88 to 95
Explanation
Apply the two specified volume reductions successively: $V_f=100^3(0.9)(0.9)=0.81\times100^3$. For a geometrically similar cube, $a_f=100(0.81)^{1/3}=\mathbf{93.22}$ mm. Volume percentages must be converted through the cube root to obtain linear shrinkage.