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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

Cavalieri principle: two solids have equal volume if:

Answer: Every horizontal cross-section at same height has equal area.

  • A They have the same total surface area
  • B Every horizontal cross-section at same height has equal area
  • C They have the same height measured from base to apex
  • D They share the same radius at their widest cross-section

Correct answer: B. Every horizontal cross-section at same height has equal area

Explanation: Cavalieri principle: if two solids lying between parallel planes have equal cross-sections at every level, they have equal volumes.

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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