RRB ALP 2013 Ques 20
Question: The ratio of the radius and height of a cone is $ 5:12 $ , respectively. Its volume is $ 314cm^{3} $ . Find its slant height.
Options:
A) 13 cm
B) 14 cm
C) 17 cm
D) 26 cm
Show Answer
Answer:
Correct Answer: A
Solution:
- Let radius and height of a cone are $ 5x $ and $ 12xcm $ respectively, then $ \frac{1}{3}\times \pi \times {{(5x)}^{2}}\times 12x=314 $
$ \Rightarrow $ $ 3.14\times 25x^{2}\times 4x=314 $
$ \Rightarrow $ $ x^{3}=\frac{314}{314}=1 $
$ \therefore $ $ x=1 $ Since, radius and height will be $ 5cm $ and $ 12cm $ . Now, slan height, $ l=\sqrt{h^{2}+r^{2}}=\sqrt{{{(12)}^{2}}+{{(5)}^{2}}}=\sqrt{169}=13cm $
BETA
