Similar Figures and Volume Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 1 of 51 of 5 Items 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 = l w h3 (1 point) ft.3 Remaining Attempts : 3 Skip to navigation page 13 of 14

Answer 1

To find the volume of a pyramid, the formula used is:

\[ V = \frac{1}{3} l w h \]

Where:

• \( V \) is the volume,
• \( l \) is the length of the base,
• \( w \) is the width of the base, and
• \( h \) is the height of the pyramid.

When you dilate a figure by a scale factor, the volume changes by the cube of that scale factor. In this case, the scale factor is 2.

This means that the new volume \( V' \) can be calculated as:

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

Where \( k \) is the scale factor, so \( k = 2 \) in this case.

Thus,

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

If you know the original volume \( V \) of the pyramid, you can calculate the new volume by multiplying it by 8.

For example, if the original volume \( V \) was 10 ft³, the new volume would be:

\[ V' = 8 \times 10 = 80 \text{ ft}^3 \]

Make sure to use the original volume of the pyramid provided in the question to find the new volume after the dilation.