Answered

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?

Verified Answer :

nobillionaireNobley

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

kudzordzifrancis

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,

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


\(Number\:of\:cubes=20\times8\)


\(Number\:of\:cubes=160\)





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