Conversion of one solid into another
When one solid is melted, recast, or reshaped into another solid without wastage, the volume of material remains the same.
Practice This ConceptMain explanation
Teacher explanation
In conversion problems, the important idea is conservation of material. The shape changes, but the amount of material does not change if nothing is lost. So the volume of the old solid is set equal to the volume of the new solid, and then the missing dimension is found.
Example
If a metal sphere is recast into a cylinder without loss, we write volume of sphere = volume of cylinder and solve for the unknown radius or height.
Simple analogy
Recast means same material, same volume.
Common confusion
Students often compare surface areas instead of volumes, or they forget that the total material stays the same.
Exam tip
In recasting questions, write volume before and after as equal, then substitute the correct formulas.
Answer writing and exam use
1-mark use
Write the exact meaning of conversion of one solid into another in one clean line.
2-mark use
Define conversion of one solid into another and add one example or condition.
3-mark use
Explain conversion of one solid into another, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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