Question

The largest cone is curved out from one face of solid cube of side $21cm$. Find the volume of the remaining solid.

Answer 1

As seen in the figure the maximum volume of cone that can be carved will be of radius = 0.5side length of cube

$R=0.5L=0.5\times 21=10.5cm$

h=21cm

$V=\frac{1}{3}\pi R^{2}h=\frac{1}{3}\pi \times {10.5}^2\times 21=2424.52c{m}^3$

Volume of wood left= Volume of cube-V

$V_l=l^3-V={21}^3-2424.52={21}^3-2424.52=6836.5c{m}^3$