Question

Determine the ratio of the largest length of rods that can be fitted in a sphere and cube, given that the sphere exactly fits inside the cube.

• A. $\sqrt{3}:1$
• B. $1:\sqrt{3}$
• C. 1:1
• D. 2:1

Answer 1

The correct option is B

$1:\sqrt{3}$

Let the side of the cube be $x$.
So, diameter of sphere$=x$
Now, largest rod in cube$=\sqrt{3}x$ and largest rod in sphere is diameter itself, i.e., $x$,

which is also equal to the side of the cube if the sphere exactly fits inside the cube.
$\therefore$ Ratio$=\frac{x}{\sqrt{3}x}=\frac{1}{\sqrt{3}}$