The sum of the circumferences of two circles is 42 pie cm and the sum of their areas is 225 pie cm^2. Find the radius of each circle?

Answer 1

Let the radius of the first circle be r1 and the radius of the second circle be r2.

We know that the circumference of a circle is given by 2πr and the area of a circle is given by πr^2.

Given that the sum of the circumferences is 42π, we have:
2πr1 + 2πr2 = 42π
=> 2π(r1 + r2) = 42π
=> r1 + r2 = 21

Given that the sum of the areas is 225π, we have:
πr1^2 + πr2^2 = 225π
=> r1^2 + r2^2 = 225

Now, we can use the equations r1 + r2 = 21 and r1^2 + r2^2 = 225 to solve for the values of r1 and r2.

From r1 + r2 = 21, we can write:
r1 = 21 - r2

Substitute this into r1^2 + r2^2 = 225:
(21 - r2)^2 + r2^2 = 225
=> 441 - 42r2 + r2^2 + r2^2 = 225
=> 2r2^2 - 42r2 + 216 = 0
=> r2^2 - 21r2 + 108 = 0
=> (r2 - 9)(r2 - 12) = 0

So, r2 = 9 or r2 = 12.

If r2 = 9, then r1 = 21 - 9 = 12.
If r2 = 12, then r1 = 21 - 12 = 9.

Therefore, the radius of the first circle is 12 cm and the radius of the second circle is 9 cm.