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
[tex]z^{2}=\frac{x}{y}[/tex]
we ahve
[tex]x=200\pi \ m^{2}[/tex]
[tex]y=2\pi \ m^{2}[/tex]
substitute
[tex]z^{2}=\frac{200\pi}{2\pi}[/tex]
[tex]z^{2}=100[/tex]
[tex]z=10[/tex]
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
