It's given in the question,
- Side length of the smaller cube is [tex]x^6[/tex] units.
- Side length of the larger cube is [tex]3x^6[/tex] units.
We have to find the number of smaller cubes that can be fitted in the larger cube.
Volume of cube is given by the formula,
Volume = (side)³
Volume of the larger cube = [tex](3x^6)^3[/tex]
= [tex]27x^{18}[/tex] units³
Volume of the smaller cube = [tex](x^6)^3[/tex]
= [tex]x^{18}[/tex] units³
Let the number of smaller cube that can be fitted in the larger cube = [tex]n[/tex]
Volume of [tex]n[/tex] cubes = [tex]nx^{18}[/tex] units³
If space inside the larger cube will be occupied by 'n' smaller cubes,
volume of [tex]n[/tex] smaller cubes = Volume of a larger cube
[tex]n(x^{18})=27x^{18}[/tex]
[tex]n=27[/tex]
Therefore, [tex]27[/tex] smaller cubes can be fitted in the larger cube.
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