A sphere passes through the eight corners of a cube of side 14 cm. Fi…

We know that,

Diagonal of cube = \(\sqrt {3}\) × Side of cube

volume of the sphere = \(\frac{4}{3}\)πr³

We have,

Side of the cube = 14cm

According to the question,

Diagonal of the cube = Diameter of the sphere

So, Diagonal of cube = \(\sqrt {3}\) × 14 = 14\(\sqrt {3}\) cm

Now the radius of the sphere = \(\frac{14\sqrt {3}}{2}\) = 7\(\sqrt {3}\)

Now the volume of the sphere = \(\frac{4}{3}\) × \(\frac{22}{7}\) × (7\(\sqrt {3}\))³

= $4312\sqrt{3}$