Answer: [tex]28\ cubes[/tex]
Step-by-step explanation:
The volume of a cube can be found with this formula:
[tex]V_{(c)}=s^3[/tex]
Where "s" is the lenght of any edge of the cube.
The formula for calculate the volume of a rectangular prism is:
[tex]V_{rp}=lwh[/tex]
Where "l" is the lenght, "w" is the width and "h" is the height.
We need to find the volume of a cube box:
[tex]V_1=s^3=(\frac{1}{6}ft)^3=\frac{1}{216}ft^3[/tex]
To find the volume of the shipping box, first we must convert the mixed number to an improper fraction:
[tex]1\frac{1}{6}=\frac{(6*1)+1}{6}=\frac{7}{6}[/tex]
Then the volume of the shipping box is:
[tex]V_2=lwh\\\\V_2=(\frac{7}{6}ft)(\frac{1}{3}ft)(\frac{1}{3}ft)=\frac{7}{54}ft^3[/tex]
Now, in order to find the number of cube boxes can Haley fits into a shipping box, you must divide the the volume of the shipping box by the volume of one cube. This is:
[tex]\frac{\frac{7}{54}ft^3}{\frac{1}{216}ft^3}=28[/tex]
