Question

The largest sphere is carved out of a cube of side 7 cm. Then, the volume of the sphere is

• A. $179.67c{m}^3$
• B. $165.67c{m}^3$
• C. $175.67c{m}^3$
• D. $182.67c{m}^3$

Answer 1

The correct option is A $179.67c{m}^3$

The diameter of the largest sphere that can be carved out of a cube of a side 7 cm will be 7 cm.


$\Rightarrow$ Radius of the sphere is, $r=\frac{7}{2}cm$

$\therefore$ Volume of the sphere $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^3$
$=\frac{4}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}$
$=\frac{49\times 11}{3}$
$=\frac{539}{3}=179.67c{m}^3$