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