Chvorinov's rule gives the solidification time t of a casting in terms of the ratio of its volume V to surface area A as t = B(V/A)² (B is a constant set by the mold and metal). Under the same mold conditions, a cube casting 50 mm on a side solidified in 4.0 minutes. Which value is closest to the solidification time of a cube casting 100 mm on a side?

Answer: B. 16 minutes

For a cube of side a, V/A = a³/(6a²) = a/6, so V/A ≈ 8.3 mm for 50 mm and about 16.7 mm for 100 mm, exactly twice as large. The solidification time is proportional to the square of V/A, so t = 4.0 × 2² = 16 minutes. 8.0 minutes assumes the solidification time is proportional to size, and 32 minutes assumes it is proportional to volume and multiplies by 8. Larger castings take longer to solidify and have coarser structures. Because a riser (the feeder that supplies molten metal) cannot compensate for shrinkage cavities unless it solidifies after the casting, this rule is also the basis for designing risers with a larger V/A than the casting.