To prepare for warmer weather, a parent is testing out toys to see if they will sink or float in the water. The density of water is 1 gram per `cm^{3}.` The parent wants to teach their children how to dive underwater by picking up toys that sink to the bottom. The parent found a rectangular prism toy with dimensions 4 cm by 10 cm by 20 cm but has several options for the mas. To the nearest whole number, what is the smallest value of mass, in grams, that the toy could be but still sink?