Question

A cone of maximum volume is carved out of a block of wood of size $20cm\times 10cm\times 10cm$. find the volume of the cone carved out, correct to one decimal places.

Answer 1

The one of maximum volume that can be carved out of the block would be with $height=10cm,radius=10cm$

Volume of cone $=\frac{1}{3}\pi r^{2}h$

Putting the values $=\frac{1}{2}\pi {10}^2\times 10=1047.2c{m}^3$