Question

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left.(use π = \(\frac{22}7\))

Answer 1

To be the largest, diameter of the sphere = edge of the cube 

∴ its radius = \(\frac{1}2\) × edge 

= (7)³ - \(\frac{4}3π(\frac{7}2)^3\)

Volume of wood left = volume of cube – volume of sphere 

= 343 – 179.67 

= 163.33 cm³