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A cone is inverted and filled with water to 1/2 of its height.  What percent of the cone's volume is filled with water?  Express your answer as a decimal to the nearest ten-thousandth.  (You should enter 10.0000 for 10\% instead of 0.1000.)

 Jul 28, 2022
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Let \(r\) and \(h\) be the radius and height of the smaller cone, respectively. 

 

The volume of the new shape is \(\pi r^2 h \over 3\), and the volume of the old shape is \(\pi (2r)^2 2h \over 3\).

 

The answer is the volume of the new shape over the volume of the old shape. 

 

Can you take it from here?

 Jul 28, 2022

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