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GATE 2022 IN – Question 2

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A sphere of radius $r$ cm is packed in a cubical box. What is the minimum volume (in cm$^3$) of a box enclosing the sphere?

  1. $r^3/8$
  2. $r^3$
  3. $2r^3$
  4. $8r^3$

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Show answer and explanation

Correct answer: (D) $8r^3$

Explanation

Each cube side must be at least the sphere diameter 2r. A cube of side 2r just encloses it, giving volume (2r)³=**8r³, D**.