Question

The radius of the bulls-eye of the dartboard is 8 inches. The radius of each concentric circle (there are 4 labeled A, B, C, D from the inside out) is 14 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, the probability that the dart will hit in area C is what percent?

Answer 1

The formula for the area of a circle is A = πr². The area for A, the innermost circle, is A=3.14(8²)=200.96 in².
The area for B (including the area of A) is A=3.14(8+14)²=1519.76 in².
The area for C (including the areas of A and B) is A=3.14(8+14+14)²=4069.44.
The area for D (including the areas of A, B and C) is A=3.14(8+14+14+14)²=7850 in².
We now need to know how much the ring for circle C takes up. We take the entire area for C and subtract the total area for B (since it includes A):
4069.44-1519.76=2549.68 in².
To find the percent, we divide this amount by the total area of the board, 7850:
2549.68/7850=0.3248
The probability of hitting circle C would be 32.48%.