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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

A sphere of radius R is melted into n small spheres of radius r. Relation:

Answer: R³ = nr³.

  • A R = nr
  • B R³ = nr³
  • C R² = nr²
  • D nR = r

Correct answer: B. R³ = nr³

Explanation: Volume is conserved on melting: (4/3)πR³ = n×(4/3)πr³. The (4/3)π cancels, giving R³=nr³. E.g. n=8, r=1 → R³=8, R=2 (checks out). Ans: R³=nr³.

Cylinder, Cone, SphereV=πr²hCSA=2πrhV=⅓πr²hCSA=πrlV=4/3πr³SA=4πr²

Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.

Concept context

Perimeters, areas, and volumes of 2D and 3D shapes

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