Question

A rectangular prism has a length of 12 in., a width of 5 in., and a height of 4 1/4 in. The prism is filled with cubes that have edge lengths of 1/4 in. How many cubes are needed to fill the rectangular prism?

Answer 1

V = L * W * H
L = 12
W = 5
H = 4.25
V = 255 cu in

Volume of small cubes = 1/4 * 1/4 * 1/4 = 1/64

Number needed = volume of large cube / volume of small cube
Number needed = 16320.
This answer does not answer whether or not you get a possible prism.