The volume of a right circular cylinder with radius $r$ and height $h$ is calculated using the formula $\mathrm{V} = \pi r^{2} \mathrm{~h}$. Two right circular cylinders with equal heights, empty interiors, and parallel bases are nested inside each other, with two faucets on top. One of these faucets fills the inner cylinder, while the other fills the region between the cylinders, with the same amount of water per unit time. The faucets are opened simultaneously and closed when the inner cylinder is completely filled. In the final state, the height of the water in the inner cylinder is 4 times the height of the water in the region between the cylinders. Accordingly, what is the ratio of the radius of the outer cylinder to the radius of the inner cylinder? A) $\sqrt{3}$ B) $\sqrt{5}$ C) $\sqrt{7}$ D) 2 E) 3
The volume of a right circular cylinder with radius $r$ and height $h$ is calculated using the formula $\mathrm{V} = \pi r^{2} \mathrm{~h}$.
Two right circular cylinders with equal heights, empty interiors, and parallel bases are nested inside each other, with two faucets on top. One of these faucets fills the inner cylinder, while the other fills the region between the cylinders, with the same amount of water per unit time.
The faucets are opened simultaneously and closed when the inner cylinder is completely filled. In the final state, the height of the water in the inner cylinder is 4 times the height of the water in the region between the cylinders.
Accordingly, what is the ratio of the radius of the outer cylinder to the radius of the inner cylinder?
A) $\sqrt{3}$\\
B) $\sqrt{5}$\\
C) $\sqrt{7}$\\
D) 2\\
E) 3