To find out how many 3 cm cubes are required to completely fill a cuboid that measures 12 cm by 6 cm by 9 cm, follow these steps:
1. Calculate the volume of the cuboid:
The volume [tex]\( V \)[/tex] of a cuboid is given by the product of its length, width, and height.
[tex]\[
V_{\text{cuboid}} = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given the length is 12 cm, the width is 6 cm, and the height is 9 cm, we get:
[tex]\[
V_{\text{cuboid}} = 12 \, \text{cm} \times 6 \, \text{cm} \times 9 \, \text{cm}
\][/tex]
[tex]\[
V_{\text{cuboid}} = 648 \, \text{cm}^3
\][/tex]
2. Calculate the volume of a smaller cube:
The volume [tex]\( V \)[/tex] of a smaller cube is given by the cube of its side length.
[tex]\[
V_{\text{cube}} = \text{side}^3
\][/tex]
Given the side length of the smaller cube is 3 cm, we get:
[tex]\[
V_{\text{cube}} = 3 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm}
\][/tex]
[tex]\[
V_{\text{cube}} = 27 \, \text{cm}^3
\][/tex]
3. Determine the number of smaller cubes needed:
To find the number of 3 cm cubes required to fill the cuboid, divide the volume of the cuboid by the volume of the smaller cube.
[tex]\[
\text{Number of cubes} = \frac{V_{\text{cuboid}}}{V_{\text{cube}}}
\][/tex]
Substitute the volumes we have calculated:
[tex]\[
\text{Number of cubes} = \frac{648 \, \text{cm}^3}{27 \, \text{cm}^3}
\][/tex]
[tex]\[
\text{Number of cubes} = 24
\][/tex]
Therefore, it takes 24 cubes each measuring 3 cm to fill the given cuboid.
