Question

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 _______

Answer 1

Concept:

As the pattern will shrink, we will have to make larger size of a pattern than the original volume and hence we are adding the tolerance in the original dimension.

And we will subtract the volume from both pattern and original volume since there is a spherical cavity in the product

Now,

The ratio of the volume of the pattern to the volume of casting \(= \frac{{Volume\;after\;shrinkage\;allowance}}{{original\;volume}}\)

\(= \frac{{\left[ {\left( {1.03 \times 100} \right) \times \left( {1.03 \times 50} \right) \times \left( {1.03 \times 10} \right)} \right] - \frac{4}{3} \pi \times {{\left[ {1.03 \times 2} \right]}^3}}}{{\left( {100 \times 50 \times 10} \right) - \frac{4}{3} \pi \times {{\left( 2 \right)}^3}}}\)

= 1.09