Question

A rectangular prism with a volume of four cubic units is filled with cubes with side lengths of 1/3 unit.

Answer 1

Given:

Volume of rectangular prism = 4 cubic units

Side length of cube = $\frac{1}{3}$ unit

To find:

How many cubes fill in the prism.

Solution:

Volume of cube = side × side × side

                           $=\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}$

                           $=\frac{1}{27}$

$\text{Number of cubes}=\frac{\text{Volume of rectangular prism}}{\text{Volume of cube}}$

                          $=\frac{4}{\frac{1}{27} }$

Apply the fraction: $\frac{a}{\frac{b}{c}}=\frac{a \cdot c}{b}$

                          $=\frac{4 \cdot 27}{1}$

Number of cubes = 108

Therefore 108 cubes fill in the prism.