Quantitative Aptitude Ques 725
Question: A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, then the ratio of their radius and height is
Options:
A) 1: 2
B) 1 : 3
C) 2 : 3
D) 3 : 4
Show Answer
Answer:
Correct Answer: D
Solution:
- Radius of cylinder = Radius of cone = r Height of cylinder = Height of cone = h
$ \therefore $ $ \frac{Surfaceareaofcylinder}{Surfaceareaofcone}=\frac{2\pi rh}{\pi rl}=\frac{8}{5} $
$ \Rightarrow $ $ 2h=\frac{8l}{5} $
Now, $ 2h=\frac{8l}{5} $
On squaring both sides’ we get
$ 4h^{2}=\frac{8^{2}l^{2}}{5^{2}} $
$ \Rightarrow $ $ 4h^{2}=\frac{8^{2}}{5^{2}}(h^{2}+r^{2}) $
$ \Rightarrow $ $ 4h^{2}-\frac{64h^{2}}{25}=\frac{8^{2}}{5^{2}}r^{2} $
$ \Rightarrow $ $ \frac{(100-64)h^{2}}{25}=\frac{64}{25}r^{2} $
$ \Rightarrow $ $ \frac{r^{2}}{h^{2}}=\frac{36}{64} $
$ \Rightarrow $ $ \frac{r}{h}=\frac{6}{8}=\frac{3}{4} $
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