Question

A carpenter has a wooden cube of side $10cm$ Find the volume of wood should be taken out to make it sphere of maximum size

Answer 1

Side of cube $10cm$

The volume of the cube is ${10}^3=1000c{m}^3$

The diameter of the sphere is $10cm$

Radius is $5cm$

Volume of sphere is

$\frac{4}{3}\times \pi \times r^3\frac{4}{3}\times \frac{22}{7}\times 5^3\frac{4\times 22\times 125}{3\times 7}=523.8c{m}^2$

Remaining volume is $1000-523.8=476.2$