Question

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

(1 point)
cm3

Answer 1

To determine the volume of a figure when it is dilated using a scale factor, we need to understand how dilation affects volume.

When an object is dilated by a scale factor \( k \), the volume of the new figure becomes \( k^3 \) times the volume of the original figure.

First, let's find the volume of the original figure. Based on the provided dimensions of 6 cm, 8 cm, and 10 cm, it appears to be a rectangular prism. The formula for the volume \( V \) of a rectangular prism is given by:

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

Substituting the given dimensions:

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

Next, we apply the scale factor of \( k = 2 \) to find the new volume:

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

Calculating the new volume:

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

Thus, the volume of the figure after dilation is:

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