Given:
The length of the rectangular prism is 2 cm.
The width of the prism is [tex]\frac{7}{4}[/tex] cm.
The height of the prism is 1 cm.
The side lengths of the cube is [tex]\frac{1}{4}[/tex] cm.
We need to determine the number of cubes with side lengths [tex]\frac{1}{4}[/tex] would fill the prism.
Volume of the cube:
The volume of the cube can be determined using the formula,
[tex]V=s^3[/tex]
Substituting the value, we get;
[tex]V=(\frac{1}{4})^3[/tex]
[tex]V=\frac{1}{64}[/tex]
Thus, the volume of the cube is [tex]\frac{1}{64} \ cm^3[/tex]
Volume of the rectangular prism:
Volume of the rectangular prism can be determined using the formula,
[tex]V=lwh[/tex]
Substituting the values, we get;
[tex]V=2\times \frac{7}{4} \times 1[/tex]
[tex]V=3.5 \ cm^3[/tex]
Thus, the volume of the rectangular prism is 3.5 cm³
Number of cubes:
The number of cubes can be determined by dividing the volume of the prism by the volume of the cube.
Thus, we have;
[tex]No. \ of \ cubes=\frac{3.5}{\frac{1}{64}}[/tex]
[tex]No. \ of \ cubes=3.5 \times 64[/tex]
[tex]No. \ of \ cubes=224[/tex]
Thus, the number of cubes that fill the prism are 224 cubes.
