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\[\pi =3.14\])

Answer:

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 \[=\frac{1}{3}\pi {{r}^{2}}h\]

\[=\frac{1}{3}\times 3.14\times 3\times 3\times 4\]

\[=37.68\,c{{m}^{3}}\]