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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

The volume of the largest right circular cone that can be inscribed in a sphere of radius 3 is:

Answer: 32π/3.

  • A 12π
  • B 32π/3
  • C 36π
  • D 16π

Correct answer: B. 32π/3

Explanation: Maximum cone volume = (8/27) of the sphere's volume = (8/27)(4/3·π·27) = 32π/3.

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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