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GATE 2022 XH5 (Psychology) – Question 2

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

A sphere of radius $r$ cm is packed in a box of cubical shape. What should be the minimum volume (in cm$^3$) of the box that can enclose the sphere?

  1. $\frac{r^3}{8}$
  2. $r^3$
  3. $2r^3$
  4. $8r^3$

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Show answer and explanation

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

Explanation

The smallest cube that holds a sphere has a side equal to the diameter, $2r$. Its volume is $(2r)^3 = 8r^3$.