A) \[\frac{100}{3}\]
B) \[40\]
C) \[50\]
D) \[\frac{200}{3}\]
Correct Answer: C
Solution :
Let h and r be the height and radius of the cone. \[\therefore \]Volume of cone \[=\frac{1}{3}\pi {{r}^{2}}h\] and new height \[=\frac{h\times 150}{100}=\frac{3h}{2}\] \[\therefore \]Volume of cone \[=\frac{1}{3}\pi {{r}^{2}}\cdot \frac{3\,\,h}{2}=\frac{1}{2}\pi {{r}^{2}}h\] Change in volume of cone \[=\frac{1}{2}\pi {{r}^{2}}h-\frac{1}{3}\pi {{r}^{2}}h-\frac{1}{3}\pi {{r}^{2}}h=\frac{1}{6}\pi {{r}^{2}}h\] \[\therefore \]Percentage increase \[=\frac{\frac{1}{6}\pi {{r}^{2}}h}{\frac{1}{3}\pi {{r}^{2}}h}\times 100%=50%\]
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