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 the blanks above.

Answer 1

You have the volume of the cube is:

Vcube=a^3
Vcube=(1/3 inch)^3
Vcube=1/27 inch^3

The volume of a block with a side length of 1/6 inch is:

V1=1/216 inch^3

(1/27 inch^3)/(1/216 inch^3)=8 blocks with a side length of 1/6 inch

The volume of a block with a side length of 1/9 inch is:

V2=1/729 inch^3

(1/27 inch^3)/(1/729 inch^3)=27 blocks with a side length of 1/9 inch

Answer 2

8 blocks and 27 blocks.

Explanation:

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

(A) Let B block with a side length of
`((1)/(6))` inch will be required to fill the cube.

so volume of cube = volume of block B

`((1)/(3))^3` = B ×
`((1)/(6))^3`

B =
`(((1)/(3))^3)/(((1)/(6))^3)`

=
`((6)^3)/(3^3)`

=
`((6)/(3))^3`

= (2)³ = 8 blocks

(B) Let C blocks with a side length of
`((1)/(9))` inch will be required to fill the cube.

Volume of cube = total volume of blocks C

`((1)/(3))^3` =
`((1)/(9))^3` × C

C =
`((1)/(3))^3` /
`((1)/(9))^3`

=
`(9^3)/(3^3)=((9)/(3))^3=3^3`

= 27 blocks

Therefore, answer is 8 blocks and 27 blocks.