Question

A right rectangular prism has these dimensions:

Answer 1

Volume of rectangular prism = 1 1/3 x 5/6 x 2/3 = 4/3 x 5/6 x 2/3 = 20/27

Volume of cube = 1/6 x 1/6 x 1/6 = 1/216

Number of cubes that will pack the rectangular prism = 20/27 / 1/216 = 160

Answer 2

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,

$Number\:of\:cubes=\frac{20}{27} \times \frac{216}{1}$

$Number\:of\:cubes=20\times8$

$Number\:of\:cubes=160$