Question

The largest sphere is carved out of a cube of a side 7 cm. Find the volume of the sphere. (Approximate value)

• A. $180c{m}^3$
• B. $160c{m}^3$
• C. $90c{m}^3$
• D. $80c{m}^3$

Answer 1

The correct option is A

$180c{m}^3$

The diameter of the largest sphere which can be carved out of a cube of side 7 cm is 7 cm.
$\therefore$ Radius of the sphere $=r=\frac{7}{2}cm$
Hence, volume of the sphere$=\frac{4}{3}\pi r^3$
$\Rightarrow$ Volume of the sphere $=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^{3}c{m}^3$
$\Rightarrow$ Volume of the sphere $=\frac{4}{3}\times \frac{22}{7}\times \frac{343}{8}c{m}^3$
$=179.66c{m}^3$
$\approx 180c{m}^3$