# Relationship between a circle inscribed in a square and a sphere inscribed in a cylinder

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?

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