Cylindrical Containers

$\cfrac{V_{large}}{V_{small}}=\cfrac{\pi\cdot r_{large}^2\cdot h_{large}}{\pi\cdot r_{small}^2\cdot h_{small}}=\cfrac{\pi\cdot (2r_{small})^2\cdot 2h_{small}}{\pi\cdot r_{small}^2\cdot h_{small}}=2^2\cdot2=8$

$V_{large}=8V_{small}$

$\therefore$ $\boxed{8}$ small containers can be filled with water from the large containers.

Two similar objects with a side length ratio of $\frac{1}{2}$ will have a volume ratio of $\frac{1^3}{2^3} = \frac{1}{8}$ . Therefore, $\boxed{8}$ small containers are filled for every $1$ big container.

By rephrasing the conditions we see that all dimensions are multiplied by a scale factor (in each 3 dimensions) of one half so for the volume which is
( V = L x W x H ), we do: 1/2 * 1/2 * 1/2

or

1³/2³ = 1/8. 1/8 * 1 = 1/8,

so we fit 8 into the same volume.

Hence [8]