Question

A cube has a side length of 1/3 inch.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.

Answer 1

(In order of the ____ spaces)

1.) First, find the volume of the cube with a side length of
`(1)/(3)` of an inch.
`\left( (1)/(3)\right)^3 = (1)/(27).` Then, find the volume of the
`(1)/(6)` side length cube.
`\left( (1)/(6)\right)^3 = (1)/(216)`. Next, divide.
`((1)/(27))/((1)/(216))=\boxed{8}` cubes that need to fill the cube.
2.) Using the same logic, we get
`\boxed{27}`.