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The ratio of the area of a circle to the area of the square it is inscribed in is equal to ${\pi\over 4}$ and the ratio of the volume of a sphere to the volume of the cylinder it is inscribed in is $2\over 3$. Because the figure of a sphere inscribed in a cylinder is essentially a 360° rotation of the circle inscribed in the square along its vertical axis, what sort of relationships (if any) can be drawn from these two ratios?

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    $\begingroup$ You might rather consider the ratio of the volume of a sphere to the volume of the cube it is inscribed in. $\endgroup$ – Chris Leary Mar 20 at 22:11

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