A rectangular prism with a volume of 333 cubic units is filled with cubes with side lengths of / dfrac14 4 1 start fraction, 1, divided by, 4, end fraction unit.

n = 192

Step-by-step explanation:

The volume of a cube is given by the formula;

V = L³

where L = cube side

Given L as 1/4, the equation become;

V = (1/4) ³

V = 1³/4³

V = 1/64

But volume of n cube = volume of rectangular prism

Therefore,

n * 1/64 = 3

n = 64 * 3

n = 192

Therefore, 192 units is needed.