Question

The largest possible sphere is carved out from a solid wooden cube of side 7 cm
find
1) volume of the sphere
2) the percentage of wood wasted in the process.

Answer 1

Lenght of side of cube = Diameter of sphere = 7 cm
Therefore, Radius of sphere
$= \frac{4}{3} \times \pi \times { (\frac{7}{2})}^{3} \\ = \frac{4}{3} \times \frac{22}{7} \times \frac{343}{8} \\ = \frac{539}{3} or 179\frac{2}{3} {cm}^{3}$
Volume of cube
$= {(7)}^{3} = 343 {cm}^{3}$
Volume of sphere
$\frac{539}{3} {cm}^{3}$
Volume of wood wasted
$= (343 - \frac{539}{3} ) {cm}^{3} \\ = (\frac{1029 - 539}{3} ) {cm}^{3} \\ = \frac{490}{3} {cm}^{3}$
Therefore, Percentage of volume of wood wasted
$= (\frac{ \frac{490}{3} }{343} \times 100) \%\\ = ( \frac{490}{3} \times \frac{1}{343} \times 100)\%\\ = ( \frac{1000}{21} )\% \\ = 47 \frac {13} {21}\%$