• question_answer A right circular cone of radius 3 cm, has a curved surface area of $47.1\text{ }c{{m}^{2}}$. Find the volume of the cone. (use$\pi =3.14$)

 Given, radius of right circular cone $=3\text{ }cm$ and, curved surface area $=47.1\text{ }c{{m}^{2}}$ $\pi rl=47.1$ $l=\frac{47.1}{3.14\times 3}=5\,cm$ $\therefore h=\sqrt{{{l}^{2}}-{{r}^{2}}}$ $=\sqrt{{{(5)}^{2}}-{{(3)}^{2}}}$ $=\sqrt{25-9}=4\,cm$ Now,     Volume of cone $=\frac{1}{3}\pi {{r}^{2}}h$ $=\frac{1}{3}\times 3.14\times 3\times 3\times 4$ $=37.68\,c{{m}^{3}}$