Solidification time of a molten metal in a casting is proportional to (where, V = volume of metal & A = its surface area ; in the casting)

ANS:D - V²/A²

The solidification time of a molten metal in a casting is proportional to V/A2 where V is the volume of the metal and A is its surface area. Explanation:

• The solidification time of a molten metal in a casting is influenced by several factors, including the volume of the metal and the surface area available for heat transfer.
• As the volume of the metal increases, more heat needs to be extracted to solidify the entire volume.
• Conversely, as the surface area of the metal increases, more heat can be dissipated to the surrounding environment, facilitating faster solidification.
• The ratio V/A2represents the ratio of volume to surface area squared. It accounts for the competition between the volume of metal that needs to be solidified and the surface area available for heat dissipation.
• A higher ratioV/ A2​ indicates that the volume of metal is relatively larger compared to the available surface area, leading to a longer solidification time.
• Therefore, the solidification time is proportional to V/A2​.