Question 194009
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The volume of the water in the cylinder is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_w = \pi r^2h = 2000\pi]


The volume of the sphere is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_s = \frac{4\pi r^3}{3} = \frac{4000\pi}{3}]


Once you drop the sphere into the water, the water level will rise to a height that represents the volume of the water plus the sphere.


The volume of the water plus the sphere:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_T = V_w + V_s = 2000\pi + \frac{4000\pi}{3} = \frac{6000\pi}{3} + \frac{4000\pi}{3} = \frac{10000\pi}{3}]


Divide the total volume by the area of the base of the cylinder to get the height of the water:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{10000\pi}{3} \div 100\pi = \frac{100}{3}] centimeters.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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