Respuesta :

Answer:

A. 4

Step-by-step explanation:

The one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].

What is cube ?

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].

To know more about cubes click here

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