The ratio of the areas of two circles is 4/9.
a. Find the ratio of their radii.
b. The smaller circle has a radius of 12cm. Find the radius of the larger one
Let's denote the radius of the smaller circle as r1 and the radius of the larger circle as r2.
a. The ratio of the areas of two circles is given by (π*r1^2) / (π*r2^2) = 4/9. Simplifying, we get r1^2 / r2^2 = 4/9. Taking the square root of both sides, we get (r1 / r2) = 2/3. Therefore, the ratio of their radii is 2/3.
b. We are given that the radius of the smaller circle is 12cm (r1 = 12). Using the ratio we found in part a, we can set up the following equation:
12 / r2 = 2 / 3
Cross multiplying, we get:
3 * 12 = 2 * r2
36 = 2r2
r2 = 18
Therefore, the radius of the larger circle is 18cm.