Question

The cone of maximum size is carved out from a cube of edge $14cm.$ Find the Volume of the remaining solid after the cone is carved out

Answer 1

Given: Side of the cube $=14cm$

Volume of the cube $=(14{)}^3$

$=2744c{m}^3$

The biggest cone that can be carved out will be having the height of $14cm$ and diameter will be $14cm$

Hence the radius $=7cm$

Volume of biggest cone that can be carved $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 14$

$=\frac{1}{3}\times 22\times 7\times 14$

$=\frac{2156}{3}=718.66c{m}^3$

The volume of remaining solid $=2744-718.66$

$=2025.34c{m}^3$