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 $1\dfrac{1}{4}=\dfrac{5}{4}=\dfrac{10}{8} \text{ units;}$
• width $\dfrac{5}{8} \text{ units};$
• height $\dfrac{3}{4}=\dfrac{6}{8}\text{ units.}$

A unit cube has side length $\dfrac{1}{8} \text{ unit.}$ 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 $\dfrac{1}{8} \text{ unit}$ without gaps into rectangular prism.