Project ForgeManufacturing Engineering
Metal Casting
GATE 2016
Hard
Gray cast iron blocks of size 100 mm × 50 mm × 10 mm with a central spherical cavity of diameter 4 mm are sand cast. The shrinkage allowance for the pattern is 3%. The ratio of the volume of the pattern to volume of the casting is __________.
1.09(± 0.015 accepted)
Explanation
The casting's internal spherical cavity is produced by a separate core, not the pattern, so the pattern is a solid block scaled up by the linear shrinkage factor (1.03) in each dimension. Pattern volume = (103×51.5×10.3) ≈ 54,636 mm³. Casting volume = 100×50×10 - (4/3)π(2)³ ≈ 50,000-33.5 ≈ 49,966 mm³. Ratio ≈ 54,636/49,966 ≈ 1.09.
Source: GATE ME 2016 Set-2 (2016)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.