Question

Determine the volume of the figure if it were dilated using a scale factor of 2. (1 point) cm3
height 6
width 8
length 10

Answer 1

To determine the volume of a rectangular prism (which is the shape inferred from the given dimensions), the volume can be calculated using the formula:

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

Given the dimensions:
- Length = 10 cm
- Width = 8 cm
- Height = 6 cm

Calculating the volume of the original figure:

\[
\text{Volume} = 10 \, \text{cm} \times 8 \, \text{cm} \times 6 \, \text{cm} = 480 \, \text{cm}^3
\]

Now, if this figure is dilated using a scale factor of 2, the new dimensions will be:

- New length = \( 10 \, \text{cm} \times 2 = 20 \, \text{cm} \)
- New width = \( 8 \, \text{cm} \times 2 = 16 \, \text{cm} \)
- New height = \( 6 \, \text{cm} \times 2 = 12 \, \text{cm} \)

Now we can calculate the volume of the dilated figure:

\[
\text{New Volume} = \text{New length} \times \text{New width} \times \text{New height}
\]
\[
= 20 \, \text{cm} \times 16 \, \text{cm} \times 12 \, \text{cm}
\]

Calculating this gives:

\[
20 \times 16 = 320
\]
\[
320 \times 12 = 3840 \, \text{cm}^3
\]

Alternatively, you can use the property of volume scaling with dilation, which states that if a figure is dilated by a scale factor \( k \), the volume scales by \( k^3 \).

Here, since \( k = 2 \):

\[
\text{New Volume} = \text{Original Volume} \times k^3 = 480 \, \text{cm}^3 \times 2^3 = 480 \, \text{cm}^3 \times 8 = 3840 \, \text{cm}^3
\]

Thus, the volume of the dilated figure is

\[
\boxed{3840} \, \text{cm}^3
\]