Question

use the image to answer the 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=\frac{lwh}{3} )
(1 point)

Explanation:

Step1: Find the original volume

The formula for the volume of a pyramid is \(V=\frac{l\times w\times h}{3}\). Here, \(l = 12\) ft, \(w=6\) ft, \(h = 15\) ft.

$$V_{original}=\frac{12\times6\times15}{3}$$

$$V_{original}= 360\space ft^{3}$$

Step2: Use the property of dilation for volume

When a solid is dilated by a scale factor \(k\), the new volume \(V_{new}=k^{3}\times V_{original}\). Since \(k = 2\)

$$V_{new}=2^{3}\times360$$

$$V_{new}=8\times360$$

$$V_{new}=2880\space ft^{3}$$

Answer:

\(2880\)