To find the volume of the modified cube after it has been scaled by a factor of 5, follow these steps:
1. Determine the original volume of the cube:
The original volume is given as 64 cubic meters.
2. Understand how scaling affects the volume:
When a three-dimensional object, such as a cube, is scaled by a factor, the volume changes by the cube of that scaling factor.
3. Calculate the new volume:
Since the scaling factor is 5, the volume of the cube after scaling will be:
[tex]\[
\text{New Volume} = \text{Original Volume} \times (\text{Scaling Factor})^3
\][/tex]
Plug in the values:
[tex]\[
\text{New Volume} = 64 \times 5^3
\][/tex]
Calculate [tex]\( 5^3 \)[/tex]:
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
Then the new volume will be:
[tex]\[
\text{New Volume} = 64 \times 125
\][/tex]
4. Multiply to find the final answer:
[tex]\[
64 \times 125 = 8000
\][/tex]
So, the volume of the modified cube is [tex]\( \boxed{8000} \)[/tex].
