Question

A right rectangular prism has these dimensions:

Length: Fraction 1 and 1 over 3 units
Width: Fraction 5 over 6 unit
Height: Fraction 2 over 3 unit

How many cubes of side length 1 over 6 unit are required to completely pack the prism without any gap or overlap?

40

80

160

240

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

Therefore the answer is the third choice or letter C.

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

160

Step-by-step explanation:

The dimensions of the right rectangular prisms are  l=1\frac{1}{3} \;unitsw=\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