Question

Determine the volume of the figure if it were dilated using a scale factor of 2.

6 tall
8 wide
10 long

Answer 1

To determine the volume of a rectangular prism (box) and then find the volume after a dilation with a scale factor of 2, we can start with the following steps:

1. **Calculate the original volume**:
The volume \( V \) of a rectangular prism is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
In this case, the dimensions are:
- Height = 6
- Width = 8
- Length = 10

So, the original volume is:
\[
V = 10 \times 8 \times 6
\]
\[
V = 480 \text{ cubic units}
\]

2. **Calculate the volume after dilation**:
When a figure is dilated using a scale factor \( k \), the new volume \( V' \) is given by:
\[
V' = k^3 \times V
\]
For a scale factor of \( k = 2 \), we have:
\[
V' = 2^3 \times V
\]
\[
V' = 8 \times 480
\]
\[
V' = 3840 \text{ cubic units}
\]

Thus, the volume of the figure after dilation using a scale factor of 2 is **3840 cubic units**.