Question

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

Answer 1

2π m2 and 200π m2

so ratio is 1:100

Answer 2

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

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

Thus, the required similarity ratio is 1 : 10.