Question

What is the similarity ratio for two circles with areas 2pi m^2 and 200pi m^2​

Answer 1

The scale factor is equal to 10

Explanation:

we know that

If two figures are similar. then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the larger circle

y ---> the area of the smaller circle

so

`z^(2)=(x)/(y)`

we ahve

`x=200\pi \ m^(2)`

`y=2\pi \ m^(2)`

substitute

`z^(2)=(200\pi)/(2\pi)`

`z^(2)=100`

`z=10`

therefore

The scale factor is equal to 10

The radius of the larger circle is 10 times greater than the ratio of the smaller circle