Answer:
To fill the rectangular prism, 648 cubes are needed.
Step-by-step explanation:
It is given that a rectangular prism has a length of 6 cm width of 3 cm and a height of 4 1/2 cm.
The volume of a rectangular prism is
[tex]V=length\times breadth \times height[/tex]
[tex]V_1=6\times 3 \times 4\frac{1}{2}[/tex]
[tex]V_1=18 \times \frac{9}{2}[/tex]
[tex]V_1=81[/tex]
The volume of rectangular prism is 81 cm³.
The volume of a cube is
[tex]V=a^3[/tex]
Where a is the side length.
The volume of a cube with edge 1/2.
[tex]V_2=(\frac{1}{2})^3[/tex]
[tex]V_2=0.125[/tex]
To fill the rectangular prism, the required number of cubes is
[tex]n=\frac{V_1}{V_2}[/tex]
[tex]n=\frac{81}{0.125}[/tex]
[tex]n=648[/tex]
Therefore, to fill the rectangular prism, 648 cubes are needed.
