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

Answer 1

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.