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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

A circle circumscribes an equilateral triangle of side a. Circumradius R =

Answer: a/√3.

  • A a/√3
  • B a/√2
  • C a/√3 × 2
  • D a√3/3 = a/√3

Correct answer: A. a/√3

Explanation: For equilateral triangle: R = a/√3. (Using R = abc/(4×Area) = a³/(4 × √3a²/4) = a/√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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