Question

The largest possible sphere is carved out of wooden cube of side 7cm.find the volume of wood left.

Answer 1

When the largest sphere possible is carved out of a cube..........the side of the cube is the diameter of the sphere

So the diameter of the cube is 7cm and the radius is 7/2=3.5cm
And side of the cube = 7cm

The volume of the wood left after carving out the sphere is volume of cube- volume of the sphere

volume of the sphere= 4/3π$r^{3}$
                                 =4/3*22/7*7/2*7/2*7/2
                                  =11*7*7/3
                               ≈179cu.cm
 volume of the cube=7*7*7=343cu.cm

volume of the leftover wood= 343-179=    164cu.cm

The volume of the leftover wood is 164cu.cm                         

Answer 2

 wooden cube of side 7cm is the diameter of the sphere.
therefore radius =7/2cm
the remaining volume is =volume of cube-volume of sphere
                                          =a³-4/3πr³
                                          =7³-4/3*22/7*7/2*7/2*7/2
                                           =343-539/3
                                           =163.33cm³