Question

Type the correct answer In the box. If necessary, use / for the fraction bar.A cube has a side length of 1/3 inch.It would take __ (BLANK) blocks with a side length of 1/6 inch to fill the cube. It would take __(BLANK) blocks with a side length of 1/9 inch to fill the cube.

Answer 1

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.

To solve this problem

We need to consider the ratio of their volumes.

Blocks with side length 1/6 inch:

The ratio of the side lengths is
`(1/3) / (1/6) = 2.`

The ratio of the volumes is
`2^3 = 8.`

So, it would take 8 blocks with a side length of 1/6 inch to fill the cube.

Blocks with side length 1/9 inch:

• The ratio of the side lengths is
  `(1/3) / (1/9) = 3.`
• The ratio of the volumes is
  `3^3 = 27.`

Therefore, it would take 27 blocks with a side length of 1/9 inch to fill the cube.

Answer 2

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.

Step-by-step 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,

`\begin{gathered} Number\text{ of blocks required to fill 1cube}=((1)/(3))/(1)/(6) \\ =(1)/(3)*(6)/(1) \\ =2 \\ Then,\text{ the total number of blocks is,} \\ n_1=2^3 \\ =8 \end{gathered}`

Also, the number of blocks with side length of 1/9 inch required to fill 1 cube is,

`\begin{gathered} Number\text{ of blocks required to fill 1 cube}=(1)/(3)/(1)/(9) \\ =(1)/(3)*(9)/(1) \\ =3 \\ Then,\text{ the total number of blocks is,} \\ n_2=3^3 \\ =27 \end{gathered}`

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.