A family-size cereal box in the shape of a rectangular prism with dimensions of 14 in x 10 in x 3 in holds 420 cubic inches of cereal.

If the packaging is redesigned to be a cylinder with a height of 4 inches, what would be the approximate radius so that it still holds the same volume of cereal?

(Round to the nearest whole number.)
4 inches
5 inches
6 inches
7 inches