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# 3d geometry

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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