Question

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

Answer 1

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:

`\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} \\ =(5*(4)/(5)*1(3)/(5))/(((1)/(5))^3) \\ =(5*(4)/(5)*1(3)/(5))/((1)/(5))^3 \end{gathered}`

The operation is simplified below:

`\begin{gathered} =\mleft(5*(4)/(5)*(8)/(5)\mright)/(1)/(5^3) \\ =(32)/(5)*5^3 \\ =32*25 \\ =800\text{ cubes} \end{gathered}`

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