Answer:
8 blocks and 27 blocks.
Step-by-step explanation:
A cube has a side length of [tex]\frac{1}{3}[/tex] inch.
(A) Let B block with a side length of [tex](\frac{1}{6})[/tex] inch will be required to fill the cube.
so volume of cube = volume of block B
[tex](\frac{1}{3})^3[/tex] = B × [tex](\frac{1}{6})^3[/tex]
B = [tex]\frac{(\frac{1}{3})^3}{(\frac{1}{6})^3}[/tex]
= [tex]\frac{(6)^3}{3^3}[/tex]
= [tex](\frac{6}{3})^3[/tex]
= (2)³ = 8 blocks
(B) Let C blocks with a side length of [tex](\frac{1}{9})[/tex] inch will be required to fill the cube.
Volume of cube = total volume of blocks C
[tex](\frac{1}{3})^3[/tex] = [tex](\frac{1}{9})^3[/tex] × C
C = [tex](\frac{1}{3})^3[/tex] / [tex](\frac{1}{9})^3[/tex]
= [tex]\frac{9^3}{3^3}=(\frac{9}{3})^3=3^3[/tex]
= 27 blocks
Therefore, answer is 8 blocks and 27 blocks.
