Question

A right rectangular prism has these dimensions length 1 1/4 units with width 5/8 unit height 3/4 unit . How many unit cubes of side length 1/8 unit are required to pack the prism without any gaps or overload?

Answer 1

Three dimensions of a right rectangular prism are:

• length
  `1(1)/(4)=(5)/(4)=(10)/(8) \text{ units;}`
• width
  `(5)/(8) \text{ units};`
• height
  `(3)/(4)=(6)/(8)\text{ units.}`

A unit cube has side length
`(1)/(8) \text{ unit.}` Then you can pack

• 10 such lengths in the length of rectangular prism;
• 5 such lengths in the width of rectangular prism;
• 6 such lengths in the height of rectangular prism.

Therefore, you can pack 10·5·6=300 unit cubes of side length
`(1)/(8) \text{ unit}` without gaps into rectangular prism.