A) 13 cm
B) 14 cm
C) 17 cm
D) 26 cm
Correct Answer: A
Solution :
Let radius and height of a cone are\[5x\]and\[12x\,\,cm\]respectively, then \[\frac{1}{3}\times \pi \times {{(5x)}^{2}}\times 12x=314\] \[\Rightarrow \] \[3.14\times 25{{x}^{2}}\times 4x=314\] \[\Rightarrow \] \[{{x}^{3}}=\frac{314}{314}=1\] \[\therefore \] \[x=1\] Since, radius and height will be \[5\,\,cm\]and\[12\,\,cm\]. Now, slan height, \[l=\sqrt{{{h}^{2}}+{{r}^{2}}}=\sqrt{{{(12)}^{2}}+{{(5)}^{2}}}=\sqrt{169}=13\,\,cm\]
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