Question

Determine the volume of the figure if it were dilated using a scale factor of 2.
the length is 10 cm
the width is 8 cm
the height is 6 cm

Answer 1

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

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

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

First, we calculate the original volume:

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

Now, if the figure is dilated with a scale factor of 2, each dimension (length, width, height) will be multiplied by 2. Therefore:

- 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 calculate the volume of the dilated figure:

\[
\text{New Volume} = \text{New Length} \times \text{New Width} \times \text{New Height}
\]
\[
\text{New Volume} = 20 \, \text{cm} \times 16 \, \text{cm} \times 12 \, \text{cm}
\]

Calculating that step by step:

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

Thus, the volume of the figure after dilation with a scale factor of 2 is

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