The largest sphere is carved out of a cube of side $7\text{ cm}$. What is the volume of the sphere in ${\text{cm}}^3$? (Take $\pi =\frac{22}{7}$)

The diameter of the largest sphere that can be carved out of a cube is equal to the side length of the cube.Diameter of sphere, $d=7\text{ cm}$ Radius of sphere, $r=\frac{7}{2}\text{ cm}$ The volume of a sphere is given by:
$$V=\frac{4}{3}\pi r^3$$
$$V=\frac{4}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{7}{2}$$
$$V=\frac{4}{3}\times \frac{22}{7}\times \frac{343}{8}=\frac{11\times 49}{3}=\frac{539}{3}=179\frac{2}{3}{\text{ cm}}^3$$