Q1
When a solid is melted and recast into another shape, the:
Avolume remains the same
Bsurface area remains the same
Cboth volume and surface area remain the same
Dneither remains the same
CBSEClass 10 (CBSE)MathematicsCh 12 · Topic 2
Volume of Combined Solids and Conversion
Learning to calculate volume of combined solids and convert between shapes.
Core concept
For example, if a metallic sphere is melted and recast into a cylinder, the sphere's original volume [(4/3)πr³] must equal the cylinder's new volume (πR²h), allowing the cylinder's height to be calculated if its radius is known, or vice versa. This 'conservation of volume' principle during melting and recasting is a common and important problem type, testing both volume formula knowledge and algebraic equation-solving skills together.
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• Combined solid volume = sum of the volumes of its individual parts.
• Unlike surface area, no surfaces are excluded when calculating combined volume.
• When a solid is melted and recast, its volume remains the same (conservation of volume).
• Example: sphere volume = cylinder volume, when melted sphere is recast into a cylinder.