Question

if the above pyramid is dilated using a scale factor of 2, what would be the new volume? To find the volume of a pyramid, use V= lwh/3 (1 point) □ ft.^3

Answer 1

To find the new volume of the pyramid after dilation, we can use the properties of scaling.

If we dilate a three-dimensional shape by a scale factor \( k \), the new volume \( V' \) can be calculated using the formula:

\[
V' = k^3 \cdot V
\]

where \( V \) is the original volume.

Given that the scale factor \( k = 2 \), then:

\[
V' = 2^3 \cdot V = 8 \cdot V
\]

So, the new volume will be 8 times the original volume of the pyramid.

If you need to calculate the new volume based on the actual original volume, you'll need to plug in the original volume \( V \) into the formula above. For example, if the original volume \( V \) was \( x \) ft³, then the new volume would be \( 8x \) ft³.

If you have the specific dimensions or the original volume, you can calculate the exact new volume. Otherwise, just remember it will be 8 times the original volume after dilation.