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The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 5in. width is 4/5and the height is 1 3/5the cube side is 1/5

Sagot :

Answer:

Explanation:

The dimensions of the rectangular prism are:

• Length = 5in.

,

• Width = 4/5 in.

,

• Height =1 3/5 in.

The cube has a side length of 1/5 inches.

The number of cubes to pack the prism is determined using the formula below:

[tex]\begin{gathered} \text{Number of Cubes=}\frac{\text{Volume of }Rec\tan gular\text{ Prism}}{\text{Volume of one cube}} \\ =\frac{\text{lwh}}{s^3} \\ =\frac{5\times\frac{4}{5}\times1\frac{3}{5}}{(\frac{1}{5})^3} \\ =(5\times\frac{4}{5}\times1\frac{3}{5})\div(\frac{1}{5})^3 \end{gathered}[/tex]

The operation is simplified below:

[tex]\begin{gathered} =\mleft(5\times\frac{4}{5}\times\frac{8}{5}\mright)\div\frac{1}{5^3} \\ =\frac{32}{5}\times5^3 \\ =32\times25 \\ =800\text{ cubes} \end{gathered}[/tex]

800 cubes are required to completely pack the prism without any gap or overlap.

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