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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

3 answers

The formula you provided to find the volume of a pyramid is incorrect. The correct formula for the volume \( V \) of a pyramid is:

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

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

When a three-dimensional object is dilated by a scale factor \( k \), the volumes of the original and dilated objects are related by the cube of the scale factor. Therefore, if the original volume is \( V \), the new volume \( V' \) after dilation by a scale factor of \( k \) is given by:

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

In your case, if the scale factor is \( 2 \):

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

This means the new volume will be 8 times the original volume. If you know the original volume, just multiply it by 8 to find the new volume. If you have a specific original volume, please provide it, and I can calculate the new volume for you.

what the answer

To provide you with the new volume after dilation, I need the original volume of the pyramid. However, I can show you how to calculate it based on a hypothetical original volume.

Example:

  1. Let's say the original volume \( V \) of the pyramid is \( 10 , \text{ft}^3 \) (this is just an example; you should replace it with the actual volume of your pyramid if you have it).

  2. The scale factor \( k = 2 \).

  3. Calculate the new volume \( V' \) using the formula:

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

  4. If \( V = 10 , \text{ft}^3 \):

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

So, if the original volume were \( 10 , \text{ft}^3 \), the new volume after dilation would be \( 80 , \text{ft}^3 \).

Please provide the original volume (if you have it) for a specific answer!