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?

Question

Mathematics

Guest

7 July, 22:29

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?

+1

Answers (1)

Know the Answer?

Thaddeus Cameron · 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%.