The GATE Grind

GATE 2022 CY – 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 (cm$^3$) of the box that can enclose the sphere?

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

Practise this question in The GATE Grind →

Show answer and explanation

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

Explanation

The sphere diameter is 2r, so each edge of the smallest enclosing cube must be at least 2r. A cube with exactly that edge encloses the sphere and is minimal. Its volume is(2r)³=**8r³, D**.