10th Class Mathematics Solved Paper - Mathematics-2016 Delhi Term-II Set-II

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


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