• Math

  Volume of Sphere

  Posted by Aakash on June 23, 2023 at 7:00 pm

  A solid sphere and a hollow sphere have the same outer radius. The solid sphere has a volume of 36π cubic units, while the hollow sphere has a volume of 16π cubic units. What is the ratio of the inner radius of the hollow sphere to the outer radius?

  Bikesh Sharma replied 1 year, 3 months ago 2 Members · 1 Reply
• 1 Reply

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  Bikesh Sharma

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  June 23, 2023 at 8:26 pm

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  Given

  →The outer radius of solid sphere and hollow sphere are same

  →So we Consider outer Radius of solid sphere and hollow sphere is R

  →Volume of solid sphere = 36π cubic unit

  →Volume of hollow sphere = 16π cubic unit

  To Find

  →The inner radius of the hollow sphere to the outer radius

  Assume

  →Inner radius of hollow sphere = r

  Formula

  →Volume of Solid Sphere = 4/3πR³

  →Volume of Hollow Sphere = 4/3πR³ – 4/3πr³

  Now Take

  Volume of solid sphere = 36π cubic unit

  → 4/3πR³ = 36π

  Volume of hollow sphere = 16π cubic unit

  → 4/3πR³ – 4/3πr³ = 16π

  →36π – 4/3πr³ = 16π

  →36π – 16π = 4/3πr³

  →20π = 4/3πr³

  →5×3 = r³

  →r³ = 15

  Now Take Volume of solid sphere

  →4/3πR³ = 36π

  →R³ = 27

  According to question

  →r³/R³ = 15/27

  →r/R = ³√(15/27)

  Answer

  →r/R = ³√(15/27)
  

  • This reply was modified 1 year, 3 months ago by  Bikesh Sharma.

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