A target with a diameter of cm has 4 scoring zones formed by concentric circles. The diameter of the center circle is cm. The width of each ring is cm. A dart hits the target

Question

A target with a diameter of 42 cm has 4 scoring zones formed by concentric circles. The diameter of the center circle is 6 cm. The width of each ring is 6 cm. A dart hits the target at a random point. Find the probability that it will hit a point in the blue region.

Answer 1

Answer 2

Ignor the green area which is outside the circular target and assume the dart hits somewhere randomly in the circular area.

Total area = pi(21^2) = 441pi

Blue area = pi(15^2) - pi(9^2) = 225pi - 81pi = 144pi

Fraction of area that is blue = 144pi/441pi = 16/49 = .326531 rounded to 5 places. This is the probability that a dart randomly landing in the 4 colored circular area will land in the blue region.