Scale factor lab

<p>To recover a positive length factor from an area factor, take the square root. From a volume factor, take the cube root. Work with the ratio in one direction throughout.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Given ratio, small : large</strong></th><th style="text-align: center; --cell-justify: center"><strong>Length ratio</strong></th><th style="text-align: center; --cell-justify: center"><strong>Another measure</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Areas \(9:25\)</td><td style="text-align: center; --cell-justify: center">\(3:5\)</td><td style="text-align: center; --cell-justify: center">Perimeters \(3:5\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Volumes \(8:27\)</td><td style="text-align: center; --cell-justify: center">\(2:3\)</td><td style="text-align: center; --cell-justify: center">Surface areas \(4:9\)</td></tr></tbody></table></div></div>
<p>An increase of \(20\%\) in every length means \(k=1.2\). The volume factor is \(1.2^3\), not \(1+3(0.2)\). Convert the resulting factor back to a percentage change.</p>

To recover a positive length factor from an area factor, take the square root. From a volume factor, take the cube root. Work with the ratio in one direction throughout.

An increase of \(20\%\) in every length means \(k=1.2\). The volume factor is \(1.2^3\), not \(1+3(0.2)\). Convert the resulting factor back to a percentage change.

Recovering a length factor

Recovering a length factor

Given ratio, small : large	Length ratio	Another measure
Areas \(9:25\)	\(3:5\)	Perimeters \(3:5\)
Volumes \(8:27\)	\(2:3\)	Surface areas \(4:9\)