question_answer

The largest right circular cone is carved out of a cube whose edge is of length 'p' units. Find the volume of the cone.

A)  \[\frac{\pi {{p}^{3}}}{12}cu.units\]         

B)  \[\frac{\pi {{p}^{3}}}{4}cu.units\]

C)  \[\pi {{p}^{3}}cu.units\]              

D)         \[\frac{\pi {{p}^{3}}}{5}cu.units\]

Correct Answer: A

Solution :

Volume of the cone\[=\frac{1}{3}\pi {{r}^{2}}h\] \[=\frac{1}{3}\times \pi \times {{\left( \frac{p}{2} \right)}^{2}}\times p=\frac{\pi {{p}^{3}}}{12}cu.\,units\]