The number of cubes needed are 108.
We have -
A rectangular prism of volume 4 cubic units.
We have to determine -
How many cubes of side 1/3 units are needed to fill the prism completely.
What is th formula to calculate the volume of a cube of side length 'a' units?
The volume of the cube will be -
V = (a x a x a) cubic units
According to question, we have -
Volume of Prism = 4 cubic units.
Assume that the number of cubes of side 1/3 required to fill the prism be x. The volume of x cubes will have to be equal to that of the volume of the prism.
Volume of a cube given = [tex]\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}[/tex]
Then, the Volume of x cubes will be = [tex]\frac{x}{27}[/tex]
Equating volume, we get -
[tex]\frac{x}{27} = 4[/tex]
x = 27 x 4 = 108
Hence, the number of cubes needed are 108.
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