the ratio of areas of two circles is 4/9 the smaller circle has radius of 12 cm what is the radius of the larger one

Answer 1

Let's assume that the larger circle has a radius of R cm.

The ratio of the areas of the two circles is given as 4/9, so we can set up the following equation:

(Area of Larger Circle) / (Area of Smaller Circle) = 4/9

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Plugging in the given radius for the smaller circle (12 cm), we have:

(πR^2) / (π(12)^2) = 4/9

Simplifying the equation, we can divide both sides by π:

R^2 / (12^2) = 4/9

Cross-multiplying, we have:

9R^2 = 4 * (12^2)

9R^2 = 4 * 144

9R^2 = 576

Divide both sides by 9:

R^2 = 576 / 9

R^2 = 64

Taking the square root of both sides, we have:

R = √64

R = 8

Therefore, the radius of the larger circle is 8 cm.