two concentric circle with the ratio of radii as 2:3, what is the ratio of the area?
thanks
area has the ratios squared, so 2^2:3^2 = 4:9
To find the ratio of the areas of two concentric circles with radii in the ratio of 2:3, you can use the formula for the area of a circle, which is given by A = πr^2.
Let's assume the smaller circle has a radius of 2x, where x is a positive constant. Therefore, the larger circle will have a radius of 3x, as per the given ratio.
The formula for the area of the smaller circle is A1 = π(2x)^2 = 4πx^2.
Similarly, the formula for the area of the larger circle is A2 = π(3x)^2 = 9πx^2.
Now, we can calculate the ratio of the areas A2/A1:
A2/A1 = (9πx^2)/(4πx^2) = 9/4.
So, the ratio of the areas of the two concentric circles is 9:4.
In general, when the radii of two concentric circles are in the ratio of a:b, the ratio of their areas will be a^2:b^2.