Practicing Success
A sphere passes through the eight corners of a cube of side 14 cm. Find the volume (in cm3 ) of the sphere. Take π = 22/7 |
$4312\sqrt{3}$ $4012\sqrt{3}$ $4312\sqrt{2}$ $4012\sqrt{2}$ |
$4312\sqrt{3}$ |
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 = $4312\sqrt{3}$ |