Respuesta :
Answer:
The number of cubes that fill the prism is 24
Step-by-step explanation:
Given as :
The length of cube (l) = [tex]\frac{1}{3}[/tex] cm
The length of prism (L) = 1 cm
The width of prism (w) = 2 [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{3}[/tex] cm
The height of prism (h) = [tex]\frac{2}{3}[/tex] cm
Let the number of cubes that fill the prism = x
Now, Volume of cube with length (l) = l³ cm³
Or, Volume of cube with length (l) = [tex](\frac{1}{3})^{3}[/tex] cm³
Or, Volume of cube with length (l) = [tex](\frac{1}{27})[/tex] cm³
Again , Volume of prism = [tex]\frac{1}{2}\times Length \times width \times height[/tex]
Or, Volume of prism = [tex]\frac{1}{2}\times 1 \times \frac{8}{3} \times \frac{2}{3}[/tex]
Or, Volume of prism = [tex](\frac{8}{9})[/tex] cm³
So , The number of cubes to fill prism
The number of cubes × Volume of cube = Volume of prism
Or, x × [tex](\frac{1}{27})[/tex] cm³ = [tex](\frac{8}{9})[/tex] cm³
or x = [tex]\frac{8\times 27}{9}[/tex] = 24
Hence The number of cubes which fill the prism is 24 Answer
