12.7 Ratio of Volumes

Recall from Ch 10 the idea behind Ratio of Perimeter (Scale Factor) and Ratio of Areas

Ratio of Perimeter =  $\frac{a}{b}$  

Ratio of Areas =  $\frac{a^2}{b^2}$  

What do you think the ratio of volumes would be?

 $\frac{a^3}{b^3}$  

Take our original  $\frac{a}{b}$  and cube both top and bottom

Let's say our RoP is  $\frac{5}{7}$  , our Ratio of Volume would be  $\frac{5^3}{7^3}\rightarrow\ \frac{125}{343}$  

What is the opposite of cubing something?

Taking the cube root of something! Let's say our ratio of volume is  $\frac{343}{1331}$  

 $\frac{343}{1331}\rightarrow\ \frac{^3\sqrt{343}}{3\sqrt{1331}}\rightarrow?$   

 $\frac{7}{11}$