Question

What is the similarity ratio for two circles with areas 2π m2 and 200π m2?

Answer 1

Answer:  The required similarity ratio is 1 : 10.

Step-by-step explanation:  We are given to find the similarity ratio for the two circle with areas as follows:

$A_1=2\pi~\textup{m}^2,\\\\A_2=200\pi~\textup{m}^2.$

Finding a similarity ratio for two circles is equivalent to finding the ratios of their radii.

Let, $r_1$ and $r_2$ be the radii of the two circles with areas $A_1$ and $A_2$ respectively.

So, we have

$\dfrac{A_1}{A_2}=\dfrac{2\pi}{200\pi}\\\\\\\Rightarrow \dfrac{2\pi r_1^2}{2\pi r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1^2}{r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1}{r_2}=\dfrac{1}{10}~~~~~\textup{[taking square root on both sides]}\\\\\\\Rightarrow r_1:r_2=1:10.$

Thus, the required similarity ratio is 1 : 10.

Answer 2

2π m2 and 200π m2

so ratio is 1:100