A) The ratio of height to radius of the cylinder is idependent of x only
B) The ratio of height to radius of the cylinder is independent of y only
C) Either [a] or [b]
D) Neither [a] and [b]
Correct Answer: D
Solution :
Curved surface area of cylinder \[2\pi rh=x\] Volume of cylinder = \[\pi {{r}^{2}}h=y\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{2\pi rh}{\pi {{r}^{2}}h}=\frac{x}{y}\Rightarrow r=\frac{2y}{x}Also,\,\,\,h=\frac{x}{2\pi r}\] \[\therefore \] Required ratio = \[\frac{h}{r}=\frac{\frac{x}{2\pi r}}{\frac{2y}{x}}\] \[\frac{x}{2\pi \frac{2y}{x}}\times \frac{x}{2y}=\frac{{{x}^{3}}}{8\pi {{y}^{2}}}\] So, the ratio is not independent of x or y
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