How many cubes of side length Fraction 1 over 4 unit are required to completely pack the prism without any gap or overlap?

36 cubes

Step-by-step explanation:

Dimension of rectangular prism :

Length: Fraction 1 and 1 over 2 units,

Width: Fraction 1 over 2 unit

Height: Fraction 3 over 4 unit

Volume of rectangular prism, V = Length * width * height

V = 1 1/2 * 1/2 * 3/4

V = 3/2 * 1/2 * 3/4 = 9 / 16 unit³

Volume of cube :

Side length of cube, s = 1/4

Volume, V = s³ = (1/4 * 1/4 * 1/4) = 1/64 units

Number cubes required :

9/16 ÷ 1/64

9/16 * 64/1 = 576 / 16 = 36

36 cubes are required.