Given:
Dimensions of a block are [tex]\dfrac{1}{3}\times 1\times 1[/tex].
To find:
The number of block that can be fit in a unit cube.
Solution:
Volume of a cuboid is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth or width and h is the height of the cuboid.
So, the volume of the given block is:
[tex]V_1=\dfrac{1}{3}\times 1\times 1[/tex]
[tex]V_1=\dfrac{1}{3}[/tex]
Dimensions of a unit cube are [tex]1\times 1\times 1[/tex]. So, the volume of the unit cube is:
[tex]V_2=1\times 1\times 1[/tex]
[tex]V_2=1[/tex]
We need to divide the volume of unit cube by the volume of a block to find the number of block that can be fit in a unit cube.
So, the number of blocks that fit in a unit cube is:
[tex]n=\dfrac{V_2}{V_1}[/tex]
[tex]n=\dfrac{1}{\dfrac{1}{3}}[/tex]
[tex]n=3[/tex]
Therefore, the correct option is B.
