The largest sphere is carved out of a cube of side 10.5 cm.

Side of cube = 10.5 cm

Volume of sphere = v

Diameter of the largest sphere = 10.5 cm

2r = 10.5

Volume of sphere $=4 / 3 \pi r^{3}=4 / 3 \times 22 / 7 \times 5.25 \times 5.25 \times 5.25$

$\mathrm{v}=\frac{11 \times 441}{8} \mathrm{~cm}^{3}$

$v=606.375 \mathrm{~cm}^{3}$

r = 5.25 cm