Question

What's the volume of the space remaining inside the cube if a sphere of maximum possible dimension is inscribed inside the cube of side length 21 $cm$?

• A. $4410c{m}^3$
• B. $4851c{m}^3$
  
• C. $9261c{m}^3$
  
• D. $6261c{m}^3$
  

Answer 1

The correct option is A $4410c{m}^3$

We know that,
Volume of cube
$=(side{)}^3$
Volume of sphere
$=\frac{4}{3}\pi r^3$

Given that,
Side length of cube is 21 $cm$ and sphere of maximum dimension is inscribed inside the cube.
$\therefore radiusofsphere=\frac{sidelengthofcube}{2}$

Now,
volume of cube
$={21}^3$
$=9261c{m}^3$

volume of sphere
$=\frac{4}{3}\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times \frac{21}{2}$
$=4851c{m}^3$

Hence, the volume of space remaining inside the cube
$=volumeofcube-volumeofsphere$
$=9261-4851$
$=4410c{m}^3$