Answer:
The number of cubes required is [tex]160[/tex].
Step-by-step explanation:
The dimensions of the right rectangular prisms are
[tex]l=1\frac{1}{3} \;units[/tex]
[tex]w=\frac{5}{6} \;units[/tex]
[tex]h=\frac{2}{3} \;units[/tex]
The volume of the right rectangular prism is
[tex]V=l\times b\times h[/tex].
We substitute the dimensions to get,
[tex]V=1\frac{1}{3}\times \frac{5}{6}\times \frac{2}{3}[/tex].
We convert the first mixed number to improper fraction,
[tex]V=\frac{4}{3}\times \frac{5}{6}\times \frac{2}{3}[/tex].
We multiply out to obtain,
[tex]V=\frac{40}{54}[/tex]
[tex]V=\frac{20}{27}[/tex] cubic units.
We need to determine the volume of the cube of side length,
[tex]l=\frac{1}{6}[/tex] units.
The volume of a cube is given by,
[tex]V=l^3[/tex]
This implies that,
[tex]V=(\frac{1}{6})^3[/tex]
This gives us,
[tex]V=\frac{1}{216}[/tex] cubic units.
We now divide the volume of the right rectangular prism by the volume of the cube to determine the number of cubes required.
[tex]Number\:of\:cubes=\frac{\frac{20}{27} }{\frac{1}{216} }[/tex]
We simplify to get,
[tex]Number\:of\:cubes=\frac{20}{27} \div \frac{1}{216}[/tex]
This implies that,
[tex]Number\:of\:cubes=\frac{20}{27} \times \frac{216}{1}[/tex]
[tex]Number\:of\:cubes=20\times8[/tex]
[tex]Number\:of\:cubes=160[/tex]
