f 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 a dilation with a scale factor of 2, we can use the properties of volume and scaling.

When a three-dimensional object is dilated by a scale factor \(k\), the volume changes by a factor of \(k^3\).

1. Original Volume Formula: The original volume \(V\) of a pyramid is given by: \[ V = \frac{l \cdot w \cdot h}{3} \] (where \(l\), \(w\), and \(h\) are the length, width, and height of the pyramid).

2. Scale Factor: In this case, the scale factor \(k = 2\).

3. New Volume Calculation: The new volume \(V_{new}\) after dilation will be: \[ V_{new} = V \cdot k^3 = V \cdot 2^3 = V \cdot 8 \]

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

To give you the exact numerical value of the new volume in cubic feet (ft³), you would need the original volume of the pyramid first. If you have that information, you can multiply it by 8 to find the new volume.