I was told in my class that the ratio of the area of a circle to area of a square should be greater than the ratio of the volume of a sphere to volume of a cube. But, I am not able to show this.
For the area of a circle to area of a square, I have: $\pi R^2 / R^2 = \pi$
For the volume of a sphere to volume a cube, I have: $\frac{4 \pi R^3}{3 R^3}= 4/3\pi$
But, the latter is greater than the former.
Could someone point out my error?
Thanks!