question_answer

A right-angled triangle ABC, where\[\angle B={{90}^{o}}\], is rotated about BC. If BC = 16 cm and AC = 20 cm, find the volume of the right circular cone traced out by the triangle.

A)  \[\text{2413}\,\text{c}{{\text{m}}^{\text{3}}}\]              

B)         \[\text{2311 c}{{\text{m}}^{\text{3}}}\]

C)  \[\text{1254}\,\text{c}{{\text{m}}^{\text{3}}}\]              

D)         \[\text{1725c}{{\text{m}}^{\text{3}}}\]

Correct Answer: A

Solution :

 Given, h = 16 cm and \[l=\text{ 2}0\text{ cm}.\] \[\therefore \]\[r=\sqrt{{{l}^{2}}-{{h}^{2}}}=\sqrt{{{20}^{2}}-{{16}^{2}}}\,cm\] \[=12\,cm\] \[\therefore \]Volume\[=\frac{1}{3}\pi {{r}^{2}}h\] \[=\frac{1}{3}\times \frac{22}{7}\times {{12}^{2}}\times 16\,c{{m}^{3}}\] \[=\frac{16896}{7}c{{m}^{3}}=2413\,c{{m}^{3}}\]