5 tall

18 long
4 wide

If the rectangular prism is dilated using a scale factor of 12 , what would be the volume of the dilated rectangular prism? (1 point)

1 answer

To find the volume of a rectangular prism, you can use the formula:

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

First, we calculate the volume of the original rectangular prism with the given dimensions:

  • Height (tall) = 5
  • Length (long) = 18
  • Width = 4

Calculating the volume:

\[ \text{Volume} = 18 \times 4 \times 5 \]

Calculating step by step:

\[ 18 \times 4 = 72 \] \[ 72 \times 5 = 360 \]

So, the volume of the original rectangular prism is 360 cubic units.

Next, we need to find the volume of the dilated rectangular prism after applying the scale factor of 12. When a shape is dilated by a scale factor \(k\), the new volume is given by multiplying the original volume by \(k^3\) (since volume is a three-dimensional measurement).

Here \(k = 12\), so we calculate \(k^3\):

\[ k^3 = 12^3 = 1728 \]

Now, we can find the volume of the dilated rectangular prism:

\[ \text{New Volume} = \text{Original Volume} \times k^3 = 360 \times 1728 \]

Calculating this:

\[ 360 \times 1728 = 622080 \]

Thus, the volume of the dilated rectangular prism is:

\[ \boxed{622080} \text{ cubic units.} \]