Question

The largest right circular cone is formed by cutting a wooden cubical piece of $14cm$ side. Find the volume of the cone.

Answer 1

Given,
Side of the cube $\left(a\right)=14cm$
The diameter of the largest cube cut off $=14cm$
The radius of ths coner $=\frac{14}{2}=7cm$
The height of the cone cut off $\left(h\right)=14cm.$
$\therefore$ Volume of cone $=\frac{1}{3}\pi r^{2}h$
$\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 14$
$=\frac{2156}{3}$
Hence, the volume of cubical piece cut off $=718.67{cm}^3$