How are a mold and a cast related?

The mold and the cast are related in that the mold is the object that makes the shape of the cast. Additionally they both hold the shape or part of an organism

When organisms are buried in sediment they may decay or dissolve away leaving a cavity or what we call mold, if the pace is filled with sediment, then an external cast is made. A mold fossil becomes a cast fossil when it is filled with sand or mud and hardens. A mold fossil can turn into a cast fossil, but a cast fossil cannot be a mold.

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The mold is the object that makes the shape of the cast. The cast is what is formed after you put liquid into the mold.