Question

a right rectangular prism has these dimensions length 1 and 1/2 units width 1/2 units height 3/4 units. How many cubes of side length 1/4 unit are required to completely pack the prism without any gap or overlap

Answer 1

Volume of rectangular prism = 1 1/3 x 5/6 x 2/3 = 4/3 x 5/6 x 2/3 = 20/27

Volume of cube = 1/6 x 1/6 x 1/6 = 1/216

Number of cubes that will pack the rectangular prism = 20/27 / 1/216 = 160