Which of the following expressions can be used to find how many cubes with edge length of 1/3 unit fit in a prism that is 5 units by 5 units by 8 units? Explain or show your reasoning. i. (5 x 1/3) x (5 x 1/3) x (8 x 1/3)
ii. 5 x 5 x 8
iii. (5 x 3) x (5 x 3) x (8 x 3)
iv. (5 x 5 x 8) x (1/3)

5400 cubes can be fit into the prism.

Step-by-step explanation:

We are given the dimensions of prism as:

5 units by 5 units by 8 units i.e. 5 units×5 units×8 units.

Hence, the volume of the prism is given by:

Volume of prism=5×5×8=200 cubic units

Also the edge length of cube is given by= 1/3 unit.

Hence volume of 1 cube=

Hence volume of 1 cube= (1/27) cubic units.

Let 'n' cubes can be fitted into the prism.

Hence we have the relation as:

Volume of prism=n×Volume of 1 cube.

200=n×(1/27)

n=200×27

n=5400

Hence 5400 cubes can be fitted into the prism.

 iii. (5 x 3) x (5 x 3) x (8 x 3)

Explanation:

If we ignored the smaller cubes, then the prism itself has the volume of 5 x 5 x 8 cubic units.

Now consider the smaller cubes. We can fit 3 to each unit (because 3*(1/3) = 1). This means each dimension is tripled.

We go from 5 x 5 x 8 to (5 x 3) x (5 x 3) x (8 x 3)

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