[tex]2\frac{1}{2}[/tex] or 2.5 cubes are needed to fill the rectangular prism
Solution:
A rectangular prism has:
Length = 8 inches
width = 4 inches
height = 214 inches
Find the volume of rectangular prism
[tex]volume = length \times width \times height\\[/tex]
[tex]volume = 8 \times 4 \times 214\\\\volume = 6848\ in^3[/tex]
Find the volume of cube:
[tex]volume = a^3[/tex]
Where, "a" is the length of side of cube
a = 14 inches
[tex]volume = 14^3\\\\volume = 2744\ in^3[/tex]
How many cubes are needed to fill the rectangular prism?
[tex]\text{ number of cubes } = \frac{\text{ volume of rectangular prism }}{\text{ volume of cube }}[/tex]
[tex]\text{ number of cubes } = \frac{6848}{2744} = 2.49 \approx 2.5[/tex]
Thus, [tex]2\frac{1}{2}[/tex] cubes are needed to fill the rectangular prism
