Apply scale factors to length, area, and volume using k, k^2, and k^3 relationships.
Find the new volume after a dilation
Problem
A solid with original volume \(10\) is dilated by scale factor \(3\). Find the new volume.
Big Picture
What this problem is really about
Volume tracks three independent length directions, so the dilation factor appears three times in the multiplier. We’ll cube the linear factor before touching the original volume, apply that derived multiplier once, and verify that the new-to-original volume ratio agrees with the cubic scaling rule.
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