To determine the new volume of a pyramid after dilation with a scale factor of 2, we can follow these steps:
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Understand the Scale Factor Effect on Volume: When an object is dilated with a scale factor \( k \), the volume is affected by \( k^3 \). This means if the scale factor is 2, the volume will increase by a factor of \( 2^3 = 8 \).
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Calculate the Original Volume: You have the formula for the volume of a pyramid: \[ V = \frac{lwh}{3} \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
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Calculate the New Volume: If you know the original volume \( V \), the new volume \( V' \) after dilation will be: \[ V' = 8V \]
If you have the original dimensions (length, width, and height), you can also calculate \( V \) using the formula and then multiply by 8 to find the new volume.
To summarize:
- Original Volume = \( \frac{lwh}{3} \)
- New Volume after dilation = \( 8 \times \text{(Original Volume)} \)
If you provide the dimensions \( l \), \( w \), and \( h \), I can help you calculate the exact volumes!
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