Question

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

Answer 1

Answer:

The scale factor is equal to 10

Step-by-step 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

$z^{2}=\frac{x}{y}$

we ahve

$x=200\pi \ m^{2}$

$y=2\pi \ m^{2}$

substitute

$z^{2}=\frac{200\pi}{2\pi}$

$z^{2}=100$

$z=10$

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