To determine the new volume of a pyramid after it has been dilated by a scale factor of 2, we can follow these steps:
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Start with the formula for the volume of a pyramid: \[ V = \frac{1}{3} l w h \] where \( l \) is the length of the base, \( w \) is the width of the base, and \( h \) is the height of the pyramid.
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When the pyramid is dilated by a scale factor of 2, each linear dimension (length, width, height) is multiplied by 2.
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Consequently, the new dimensions will be:
- New length: \( l' = 2l \)
- New width: \( w' = 2w \)
- New height: \( h' = 2h \)
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The new volume \( V' \) of the dilated pyramid can be calculated as: \[ V' = \frac{1}{3} (l' w' h') = \frac{1}{3} (2l)(2w)(2h) \] \[ V' = \frac{1}{3} (8lwh) \] \[ V' = 8 \left( \frac{1}{3} lwh \right) = 8V \]
Thus, the volume of the new pyramid is 8 times the original volume.
If you provide the original volume, I can calculate the new volume if needed.
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