Given
A cube has a side length of 1/3 inch.
To fill in the blanks.
It would take ____ blocks with a side length of 1/6 inch to fill the cube. It would take _____ blocks with a side length of 1/9 inch to fill the cube.
Explanation:
It is given that,
A cube has a side length of 1/3 inch.
Then, the number of blocks with side length of 1/6 inch required to fill 1 cube is,
[tex]\begin{gathered} Number\text{ of blocks required to fill 1cube}=(\frac{1}{3})\div\frac{1}{6} \\ =\frac{1}{3}\times\frac{6}{1} \\ =2 \\ Then,\text{ the total number of blocks is,} \\ n_1=2^3 \\ =8 \end{gathered}[/tex]
Also, the number of blocks with side length of 1/9 inch required to fill 1 cube is,
[tex]\begin{gathered} Number\text{ of blocks required to fill 1 cube}=\frac{1}{3}\div\frac{1}{9} \\ =\frac{1}{3}\times\frac{9}{1} \\ =3 \\ Then,\text{ the total number of blocks is,} \\ n_2=3^3 \\ =27 \end{gathered}[/tex]
Hence,
It would take 8 blocks with a side length of 1/6 inch to fill the cube. It would take 27 blocks with a side length of 1/9 inch to fill the cube.
