A) \[6{{x}^{2}}\]
B) \[18{{x}^{2}}\]
C) \[36{{x}^{2}}\]
D) \[72{{x}^{2}}\]
Correct Answer: A
Solution :
Let r and h be the radius and height of the cylinder in \[\Delta ABC.\] \[\sin 30{}^\circ =\frac{BC}{AC}\] \[\gamma =2\pi \] And \[\cos 30{}^\circ =\frac{AB}{AC}\] Or \[\frac{\sqrt{3}}{2}=\frac{x}{4\pi }\] Or \[x=2\sqrt{3}\pi \] \[\therefore \] \[2\pi r=2\sqrt{3}\pi \] Or \[r=\sqrt{3}\] and \[h=2\pi \] \[\therefore \] Volume of cylinder \[=\pi {{r}^{2}}h\] \[=\pi \times {{(\sqrt{3})}^{2}}\times 2\pi \] \[=6{{\pi }^{2}}\]You need to login to perform this action.
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