Scale factor lab

<p class="paragraph-header">Choose the measure before the multiplier</p>
<p>Geometrically similar figures have the same shape. If every corresponding length is multiplied by a positive factor \(k\), every corresponding area is multiplied by \(k^2\), and every volume by \(k^3\). Perimeters follow the length factor.</p>
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<p>The rectangles above have length factor 2, but their areas are \(2\text{ cm}^2\) and \(8\text{ cm}^2\): an area factor of 4. Doubling three perpendicular dimensions gives a volume factor of 8.</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>Measure</strong></th><th style="text-align: center; --cell-justify: center"><strong>Ratio, small : large</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Corresponding length or perimeter</td><td style="text-align: center; --cell-justify: center">\(a:b\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Area or corresponding surface area</td><td style="text-align: center; --cell-justify: center">\(a^2:b^2\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Volume or capacity</td><td style="text-align: center; --cell-justify: center">\(a^3:b^3\)</td></tr></tbody></table></div></div>
<p>Write the direction of your ratio before substituting. Similar heights alone do not prove two arbitrary solids geometrically similar; all corresponding dimensions must have the same factor.</p>

Geometrically similar figures have the same shape. If every corresponding length is multiplied by a positive factor \(k\), every corresponding area is multiplied by \(k^2\), and every volume by \(k^3\). Perimeters follow the length factor.

The rectangles above have length factor 2, but their areas are \(2\text{ cm}^2\) and \(8\text{ cm}^2\): an area factor of 4. Doubling three perpendicular dimensions gives a volume factor of 8.

Write the direction of your ratio before substituting. Similar heights alone do not prove two arbitrary solids geometrically similar; all corresponding dimensions must have the same factor.

Length, area and volume factors

Length, area and volume factors

Measure	Ratio, small : large
Corresponding length or perimeter	\(a:b\)
Area or corresponding surface area	\(a^2:b^2\)
Volume or capacity	\(a^3:b^3\)