what is the similarity ratio for two circles with areas 2pi m2 and 200pi m2
Online "^" is used to indicate exponents, x^2 = x squared.
I'm not sure what you mean by "similarity ratio," but I would assume 1/100/
Post it.
To find the similarity ratio between two circles, we need to compare their radii. The ratio between the areas of two circles is equal to the square of the ratio between their radii.
Let's assign variables to the radii of the two circles. Let's say the radius of the first circle is r1 and the radius of the second circle is r2. We are given that the areas of the two circles are 2π m² and 200π m², respectively.
The area of a circle is given by the formula A = πr². Using this formula, we can set up the following equations:
For the first circle:
2π = πr₁²
For the second circle:
200π = πr₂²
Now, let's solve these equations to find the values of r1 and r2.
First circle:
Dividing both sides of the equation by π, we get:
2 = r₁²
Taking the square root of both sides, we find:
r₁ = √2
Second circle:
Dividing both sides of the equation by π, we get:
200 = r₂²
Taking the square root of both sides, we find:
r₂ = √200
Now, let's find the ratio between the radii:
ratio = r₂ / r₁
ratio = (√200) / (√2)
ratio = √(200 / 2)
ratio = √100
ratio = 10
Therefore, the similarity ratio for the two circles is 10:1.