Question

A cubic casting of 50 mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is

1. 48.32 mm
2. 49.90 mm
3. 49.94 mm
4. 49.96 mm

Answer 1

Correct Answer - Option 1 : 48.32 mm

Concept:

Volumetric solidification shrinkage and volumetric solid contraction cause a decrease in dimensions of the casting.

Calculation:

Given:

Side of the cube, a = 50 mm, a' = Side of the cube after solidification 

Volumetric solidification shrinkage = 4%

Solid contraction = 6%

Volume of cube = (side)³ = 50³ = 125000 mm³

After considering both the allowances, the size of the cube is reduced.

V = 125000 × 0.96 × 0.94 = 112800 mm³

(a')³ = 112800

a' \(= \sqrt[3]{{112800}} = 48.32~mm\)