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The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).

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#### Solution

Diameter of sphere curved out = side of cube = 7cm or Radius =3.5cm

Volume of cube = a^{3}

=7^{3}

=343 cm^{3}

Volume of sphere`=4/3pir^3`

`= 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2 = 179.66 cm^3`

volume of the wood left=Volume of cube-volume of sphere

=343-179.66

=163.34 cm^{3}

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