Answer:
[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]
[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]
[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]
Step-by-step explanation:
Ratios and Proportions
The ratio between two numbers x and y is defined as x/y. It measures how many times y is contained in x. For example 12/8 = 1.5 means 12 is 1.5 times 8.
We have two key sets of data: the ratio between the surface areas of the cylinders and the fact that the radius and heights of the cylinders come in the same proportion.
First, we can easily compute the ratio of the surface areas
[tex]\displaystyle \frac{Area_1}{Area_2}=\frac{8\pi \ in^2 }{18\pi \ in^2}=\frac{4}{9}[/tex]
It gives us the relation
[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]
Computing the square root
[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]
Computing the cube
[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]
