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.)
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?