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 = l w h3 (1 point) ft.3 Remaining Attempts : 3 Skip to navigation. 12 ft 6 ft 15 ft

Answer 1

To calculate the new volume of a pyramid after applying a scale factor, you can follow these steps:

1. **Calculate the original volume of the pyramid** using the formula \( V = \frac{1}{3} l w h \) where:
- \( l \) = length of the base,
- \( w \) = width of the base,
- \( h \) = height of the pyramid.

Given the dimensions:
- Length (l) = 12 ft
- Width (w) = 6 ft
- Height (h) = 15 ft

Plugging in the values:
\[
V = \frac{1}{3} \times 12 \, \text{ft} \times 6 \, \text{ft} \times 15 \, \text{ft}
\]

Calculating it:
\[
V = \frac{1}{3} \times 12 \times 6 \times 15
\]
\[
V = \frac{1}{3} \times 1080 \, \text{ft}^3 = 360 \, \text{ft}^3
\]

2. **Apply the scale factor of dilation.** The volume of a three-dimensional figure is affected by the cube of the scale factor. If the scale factor is \( k \), the new volume \( V' \) is given by:
\[
V' = k^3 \times V
\]

For a scale factor of 2:
\[
k = 2 \quad \text{so} \quad k^3 = 2^3 = 8
\]

3. **Calculate the new volume:**
\[
V' = 8 \times 360 \, \text{ft}^3 = 2880 \, \text{ft}^3
\]

Thus, the new volume of the pyramid after dilation by a scale factor of 2 is \( \boxed{2880} \, \text{ft}^3 \).