Two similar circles have corresponding radii in the ratio 4:9. What is the ratio of their area
The ratio of their radii is 4:9, which means that the radius of one circle is 4x and the radius of the other circle is 9x (where x is a constant).
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Therefore, the ratio of their areas is (π(4x)^2) / (π(9x)^2).
Simplifying this expression, we get (16πx^2) / (81πx^2).
The x^2 terms cancel out, leaving us with 16/81.
Therefore, the ratio of their areas is 16:81.