question_answer

The radius of the base and height of a right circular cone are in the ratio 5 : 12. If the volume of the cone is \[314\frac{2}{7}\,c{{m}^{3}},\] the slant height (in cm) of the cone will be

A)  12                               

B)  13

C)  15                               

D)  17

Correct Answer: B

Solution :

Let the radius of the base of the cone be 5x cm and its h be12x cm. \[\therefore \]      \[V=\frac{1}{3}\pi {{r}^{2}}h\] \[\Rightarrow \]   \[314\frac{2}{7}=\frac{1}{3}\times \frac{22}{7}\times 5x\times 5x\times 12x\] \[\Rightarrow \]   \[{{x}^{3}}=\frac{2200\times 3\times 7}{7\times 22\times 25\times 12}=1\] \[\Rightarrow \]   \[x=1\] \[\therefore \] Slant height of the cone             \[=\sqrt{{{5}^{2}}+{{12}^{2}}}=\sqrt{25+144}\]             \[=\sqrt{169}=13\,cm\] Note for a right circular cone, \[{{5}^{2}}+{{12}^{2}}={{13}^{2}}\]