Poiseuille's Law gives the rate of flow, $R$, of a gas through a cylindrical pipe in terms of the radius of the pipe, $r$, for a fixed drop in pressure between the two ends of the pipe.

(a) Find a formula for Poiseuille's Law, given that the rate of flow is proportional to the fourth power of the radius.
$R =$
(Use k for any constant of proportionality you may have in your equation.)

(b) If $R=380$ cm${}^3$/s in a pipe of radius 3 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius $r$ cm.
$R =$ cm${}^3$/s

(c) What is the rate of flow of the same gas through a pipe with a 4 cm radius?
$R =$ cm${}^3$/s