Question:
The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.
Solution:
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