Question

6
8
10
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 after it has been dilated by a scale factor of 2, we can use the formula for volume dilation. When a three-dimensional object is dilated by a scale factor \( k \), its volume is multiplied by \( k^3 \).

In this case, the scale factor is 2. Therefore, the volume of the figure after dilation will be the original volume multiplied by \( 2^3 = 8 \).

To calculate the new volume after dilation, we first need to find the volume of the original figure with dimensions 6 cm, 8 cm, and 10 cm. The volume \( V \) of a rectangular prism can be calculated using the formula:

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

Plugging in the dimensions:

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

Now, to find the volume after dilation:

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

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