Aright rectangular prism has these dimensions: length 1 1/3 width 5/6 height 2/3 how many cubes of side length 1/6 unit are required to completely pack the prism without any gap or overlap?

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