A solid metal sphere of radius 6 cm is completely immersed in a vertical cylindrical vessel containing water, causing the water level to rise by 4 cm. What is the radius of the cylinder?

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Accepted Answer

1. Volume of sphere: $V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi	imes6^3=288\pi$.  
2. Water rise volume = cylinder area × rise = $\pi R^2	imes4$.  
3. Equate displaced volume: $\pi R^2\cdot4=288\pi\Rightarrow R^2=72$.  
4. So $R=\sqrt{72}=6\sqrt{2}$.  
FINAL_ANSWER: c

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