A rectangular prism with a volume of 2 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4 unit cubes does it take to fill the prism

128 cubes.

Step-by-step explanation:

Volume of each cube = (1/4) ^3 = 1/64 cubic units.

Number of cubes that will fill the prism

= 2 / 1/64

= 2*42

= 128 answer

128

Step-by-step explanation:

Method A.

The volume of the prism is 2 cubic units.

Each cube has side length of 1/4 unit.

The volume of each cube is (1/4) ^3 cubic unit.

The volume of each cube is 1/64 cubic unit.

To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.

(2 cubic units) / (1/64 cubic units) =

= 2 / (1/64)

= 2 * 64

= 128

Method B.

Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128