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 \[=\frac{1}{3}\pi {{r}^{2}}h\] \[=\frac{1}{3}\times 3.14\times 3\times 3\times 4\] \[=37.68\,c{{m}^{3}}\]
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