The area of a circular ring enclosed between two circles is 12 dm2 Find the radii of the circles if one

The area of a circular ring enclosed between two circles is 12 dm2 Find the radii of the circles if one of them is 2 times larger than the other.

Let the radius of the smaller circle be equal to a.

Then, in accordance with the conditions of our assignment, the radius of the larger circle can be expressed using 2a.

Since from the condition of our problem we know for sure that the area of a circular ring is 12 dm2, then it is possible to write down an equation and find out what the radii of these circles are equal to:

π (2а) ^ 2 – πа ^ 2 = 12;

π3a ^ 2 = 12;

a ^ 2 = 4 / π;

a1 = 2 / √π;

a2 = -2 / √π (does not fit according to the condition);

2 * 2 / √π = 4 / √π ;.

Answer: The radius of the smaller one is 2 / √π dm, and the larger one = 4 / √π dm.