Two circles with radii r and r+3 have areas that differ by 15Pi. What is the radius of the smaller circle?
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the area of a circle is pi r^2
The area of the smaller circle is pi r^2
The area of the larger circle is pi (r + 3)^2 = pi(r^2 + 6r + 9)
The difference between radiis is pi (r^2 + 6r +9) = pi r^2 = (6r + 9) pi
(6r + 9) pi = 15 pi divide by pi
6r + 9 = 15 Subtract 9 from each side
6r = 6
r = 1 This is the radius of the smaller circle
The area of the smaller circle is pi r^2
The area of the larger circle is pi (r + 3)^2 = pi(r^2 + 6r + 9)
The difference between radiis is pi (r^2 + 6r +9) = pi r^2 = (6r + 9) pi
(6r + 9) pi = 15 pi divide by pi
6r + 9 = 15 Subtract 9 from each side
6r = 6
r = 1 This is the radius of the smaller circle