CK12 - Geometry

The ratio of the volumesof two similarfiguresis equalto thecubeof the ratio betweenthe corresponding
linearsides.

Example 5

Find the ratio of the volumebetweenthe two similarfiguresC and D.

As with surfacearea,sincethe two figuresare similaryou can use the height,depth,or widthof the figures
to find the linearratio.In this examplewe will use the widthsof the two figures.

The ratio betweenthe volumesof the two figuresis thecubeof the ratio of the linearmeasurements:

Doesthis cuberelationshipagreewith the actualmeasurements?Computethe volumeof eachfigure.

As you can see, the ratio holds.We can summarizethe informationin this lessonin the followingpostulate.

SimilarSolidsPostulate: If two solidfigures,AandBare similarand the ratio of their

linearmeasurementsis , then the ratio of their surfaceareasis:

The ratio of their volumesis:

ScaleFactorsand Models

The ratio of the linearmeasurementsbetweentwo similarfiguresis calledthescalingfactor.For example,
we can find the scalingfactorfor cylindersEandFby findingthe ratio of any two correspondingmeasure-
ments.