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During conversion of a solid from one shape to another, the volume of the new shape will 

  • A.increase
  • B.decrease
  • C.remain unaltered
  • D.be doubled

Answer: C

Recasting a solid rearranges the same material into a different shape. No matter is added or removed, so the volume is conserved:

\[ V_{\text{new}} = V_{\text{old}} \]

This is the principle behind every "melted and recast" problem - it is the equation you set up first. The surface area, by contrast, does change, and usually increases when a compact shape is drawn out into a long thin one.

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