12.7 Ratio of Volumes

12.7 Ratio of Volumes

Review of Ratio of Perimeter/Ratio of Areas

• 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?

Ratio of Volumes

•  $\frac{a^3}{b^3}$  

• 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 if we have the ratio of volumes, but need the ratio of Perimeter?

• What is the opposite of cubing something?

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

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

•  $\frac{7}{11}$  

How to determine if these two shapes are similar?

• Remember, we need to find our

   $\frac{a}{b}$  ratios for each. There are many different ratios you can use. I'm going to use this set of ratios:

•  $\frac{10}{20}=\frac{14}{32}$  

• We would then cross multiply

•  $10\cdot32\ =\ 14\cdot20$  

•  $320\ =\ 280;\$  So they are NOT similar

• (You can also look at the fractions and see if they are the same value;  $\frac{10}{20}=\ \frac{1}{2}$  , but  $\frac{14}{32}\ne\frac{1}{2}$  )

Multiple Choice

Are these shapes simliar?

• Yes

• No