To determine the volume of a cube after it has been scaled, we need to understand how the volume of a cube changes when its dimensions are scaled.
1. Initial Volume: Given the initial volume of the cube is 64 cubic meters.
2. Scaling Factor: The cube is scaled by a factor of 5.
When a cube is scaled by a factor, the scaling affects all three dimensions (length, width, and height). The volume of a cube is found by cubing its side length. When the side length of a cube is scaled by a factor, the new volume is obtained by cubing the scaling factor and then multiplying by the initial volume.
Thus, the formula to find the new volume after scaling is:
[tex]\[ \text{New Volume} = \text{Initial Volume} \times (\text{Scaling Factor})^3 \][/tex]
Plugging in the given values:
[tex]\[ \text{Initial Volume} = 64 \][/tex]
[tex]\[ \text{Scaling Factor} = 5 \][/tex]
So, the new volume will be:
[tex]\[ \text{New Volume} = 64 \times (5)^3 \][/tex]
Calculating the cube of the scaling factor:
[tex]\[ (5)^3 = 5 \times 5 \times 5 = 125 \][/tex]
Then, multiply the initial volume by this result:
[tex]\[ \text{New Volume} = 64 \times 125 = 8000 \][/tex]
Therefore, the volume of the modified cube is 8000 cubic meters.
