If we have a cylinder with radius 1 and height 1 and cube with side lengths equal to 1
Volume of cube = $r^3 = 1^3 = 1$
Volume of cylinder = $\pi r^2h = \pi 1^2\times1 = \pi$
clearly $\pi > 1$, but if you think about it if you draw a square with side length one and a circle in the square, the circle has less area ( r = 1) e.g.
http://www.kevinhouston.net/blog/wp-content/uploads/2011/03/circle-in-square.png
So does this not imply that if you raise the two shapes the same height the square would be able to hold more water because the cylunder would fit into the square and there would still be space left over?
Best Answer
if your cylinder is radius 1, then the diameter is 2, so it should be bigger then a cube with side length 1. A cylinder radius 1/2 would fit inside a cube. This cylinder would have a volume of $\pi(\frac 1 2)^2\times1 = \frac \pi 4$, which is smaller than 1.