Question

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

Answer 1

To determine the volume of a figure after it has been dilated with a scale factor, we first need to find the original volume of the figure.

Given that the dimensions of the figure are 6 cm, 10 cm, and 8 cm, we can calculate the original volume as follows:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height} = 6 \, \text{cm} \times 10 \, \text{cm} \times 8 \, \text{cm}
\]

Calculating this:

\[
6 \times 10 = 60
\]
\[
60 \times 8 = 480 \, \text{cm}^3
\]

So, the original volume is \( 480 \, \text{cm}^3 \).

When the figure is dilated using a scale factor of 2, the new volume is affected by the cube of the scale factor. Therefore, we can calculate the new volume as follows:

\[
\text{New Volume} = \text{Original Volume} \times (\text{Scale Factor})^3 = 480 \, \text{cm}^3 \times 2^3
\]
\[
2^3 = 8
\]

Now we calculate the new volume:

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

Thus, the volume of the figure after dilation with a scale factor of 2 is \( \boxed{3840} \, \text{cm}^3 \).