Question

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

Answer 1

@april115

Answer 2

The similarity ratio is the ratio of the respective radii of the circles. Here the area of the circles is given by pi(200m^2). This implies that the (radius)^2 of this circle is 200m^2. Let's call this radius (r1). The other circle similarly has a (radius)^2 of 2m^2 and let's call its radius (r2). So what we are looking for is r1/r2.\[\frac{ \pi (200m^2) }{ \pi(2m^2) }=\frac{ \pi(\sqrt{200}m)^2 }{ \pi(\sqrt{2}m)^2 }=\frac{ \pi(r_{1})^2 }{ \pi(r_{2})^2 } \implies r_{1}=\sqrt{200} m,r_{2}=\sqrt2 m\] Now to find r1/r2, we just take the ratio of the radii:\[\frac{ r_{1} }{ r_{2} }=\frac{ \sqrt{200} \cancel{m} }{ \sqrt{2} \cancel{m} }=\frac{ \sqrt{200} }{ \sqrt{2} }=\sqrt{\frac{ 200 }{ 2 }}=\sqrt{100}=10\]And to give you an intuitive understanding, the similarity ratio is the ratio of the radii of the cricles. By taking the ratio of the areas, we get the (radius)^2 of one circle in the top of the fraction and the bottom has the (radius)^2. Taking the square root of the ratio of the radii squared gives first radius/second radius which is the similarity ratio. So find the radii of each circle and take its ratio.

@LatinaSenior17

Answer 3

oh wow thanks! wait so the ratio is 1:10

Answer 4

@LatinaSenior17
Medal/fan? lol =[