Question

Gray cast iron blocks $\text{200 mm × 100 mm × 10 mm}$ are to be cast in sand moulds. Shrinkage allowance for pattern making is 1%. The ratio of the volume of pattern to that of the casting will be

• A. $1.01$
• B. $1.03$
• C. $0.97$
• D. $0.99$

Answer 1

The correct option is B $1.03$

Since cast iron contracts during cooling from solid at freezing point to solid at room temperature

$\therefore \text{Shrinkage allowance = +1\%}$

$\text{Hence, shrinkage allowance given along length = 200 × 0.01 = 2 mm}$

$\text{Shrinkage allowance given along breadth = 100 × 0.01 = 1 mm}$

$\text{Shrinkage allowance given along height = 10 × 0.01 = 0.1 mm}$

$\therefore \text{Volume of pattern,}$

$V_p\text{= (200 + 2)(100 + 1)(10 + 0.1)}$

$\text{=}2.06\times {10}^{5}m{m}^3$

$\text{Volume of casting,}$

$V_C=200\times 100\times 10=2\times {10}^{5}m{m}^3$

$\therefore \frac{V_p}{V_C}=\frac{2.06\times {10}^5}{2\times {10}^5}=1.03$