Question

What is the diameter of the largest sphere which can be carved out from a cube of side x cm?

• A. One third of sum of all edges
• B. One twelfth of sum of all edges
• C. One half of sum of length of diagonals
• D. $\frac{1}{\sqrt{3}}$ times of length of any diagonal

Answer 1

Answer: (B), (D)

$\frac{1}{\sqrt{3}}$ times of length of any diagonal
One twelfth of sum of all edges

R.E.F image

Let radius of sphere be 'R'

$\Rightarrow x=2R\Rightarrow D=x$

Sum of all edges $\left(s\right)=12\times x=12x$

$\Rightarrow D=\frac{1}{12}\times s$ & $D=\frac{1}{\sqrt{3}}\times l$ $[\because l=\sqrt{3}x]$