Question

A cube has a side length of inch. It would take blocks with a side length of inch to fill the cube. It would take blocks with a side length of inch to fill the cube.

Answer 1

Complete 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.

B)It would take _ blocks with a side length of 1/9 inch to fill the cube.

Answer:

a) 8 blocks

b) 27 blocks

Step-by-step explanation:

Here we need to find the volume of the cube and volume of the block.

To find volume of the cube, let's use the formula :

V = a³

Here a = $\frac{1}{3}$

Therefore,

V =  $(\frac{1}{3})^3$

V = = $\frac{1}{27}$

Volume of the cube is $\frac{1}{27}$

To find volume of the block, let's use the formula:

V = a³

V = $(\frac{1}{6})^3$

V = $\frac{1}{216}$

To find the number of blocks, let's divide the volume of block from the volume of cube.

Therefore,

= $\frac{\frac{1}{27}}{\frac{1}{216}}$

$= \frac{1}{27} * 216$

= 8

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

B) Here we also need to find the volume of the cube and volume of the block.

To find volume of the cube, let's use the formula :

V = a³

Here a = $\frac{1}{3}$

Therefore,

V =  $(\frac{1}{3})^3$

V = = $\frac{1}{27}$

Volume of the cube is $\frac{1}{27}$

To find volume of the block, let's use the formula:

V = a³

V = $(\frac{1}{9})^3$

V = $\frac{1}{729}$

To find the number of blocks, let's divide the volume of block from the volume of cube.

Therefore,

= $\frac{\frac{1}{27}}{\frac{1}{729}}$

$= \frac{1}{27} * 729$

= 27

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