How many one-third cubes are needed to fill the gap in the prism shown below?
A. 4
B. 8
C. 16
D. 24

The one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
Cube is a [tex]3D[/tex] solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
Here we have,
Length [tex]=4\frac{2}{3}[/tex]
Breadth [tex]=4[/tex]
Height [tex]=2[/tex]
Here, we have the side of cube [tex]=\frac{1}{3}[/tex],
So, Total volume of the prism [tex]=l*b*h[/tex]
[tex]=2*4*4\frac{2}{3}[/tex]
[tex]=\frac{112}{3}[/tex]
Volume of a cube [tex]= a^{3}[/tex]
[tex]=(\frac{1}{3} )^{3}=\frac{1}{27}[/tex]
Total number of cubes [tex]= \frac{\frac{112}{3}}{\frac{1}{27} } =1008[/tex]
Volume of given cubes in prism [tex]= 32*\frac{1}{27} =\frac{32}{27}[/tex]
So, the gap left in the prism [tex]=\frac{112}{3} -\frac{32}{27} =\frac{976}{27}[/tex]
So, the number of cubes required [tex]=\frac{\frac{976}{27} }{\frac{1}{27} }=976[/tex]
Hence, we can say that the one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
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