Question

How many 1 3 inch cubes does it take to fill a box with width 2 inches, length 3 inches, and height 2 1 3 inches? Use the sketch pad to the right to show your thinking. Write your response in the box below.

Answer 1

Given a cube with side l, the volume is given by

$\text{ the volume of cube = }l^3$

In this case,

$\begin{gathered} l=\frac{1}{3}\text{ inch} \\ \text{ therefore,} \\ \text{the volume of the cube = (}\frac{1}{3})^3=\frac{1}{27}inch^3 \end{gathered}$

Given a box with width, w, length, l, and height, h, then

$\text{ the volume of the box = }lbh$

In this case,

$w=2\frac{2}{3}\text{ inch, }l=3\frac{1}{3}\text{ inch,}h=2\frac{1}{3}\text{ inch}$$\text{ the volume of the box = }2\frac{2}{3}\times3\frac{1}{3}\times2\frac{1}{3}=\frac{560}{27}inch^3$

Let the number of cubes it takes to fill the box be n, then we must have

$n=\frac{\text{ volume of the box}}{\text{ volume of the cube}}$$\begin{gathered} \text{ therefore,} \\ n=\frac{\frac{560}{27}}{\frac{1}{27}}=\frac{560}{27}\times\frac{27}{1}=560 \end{gathered}$

Therefore it will take 560 of the 1 / 3 inch cubes to fill the box