The ratio of the areas of two circle is 4/9 what is the ratio of their radii the smaller circle has a radius of 12 cm what is the ratio of the larger one
Let the radius of the larger circle be r.
The ratio of the areas of the two circles is given as 4/9.
This ratio is equal to (π*r^2) / (π*12^2), since the area of a circle is given by A = π*r^2.
Simplifying this expression, we get:
(π*r^2) / (π*12^2) = 4/9
Cancelling out the common terms, we have:
r^2 / (12^2) = 4/9
Cross-multiplying, we get:
9*r^2 = 4*(12^2)
9*r^2 = 4*144
9*r^2 = 576
r^2 = 576 / 9
r^2 = 64
Taking the square root of both sides, we get:
r = √64
r = 8 cm
Therefore, the ratio of the radii is given by 8/12, which can be simplified to 2/3.