Question

for the target shown to the right, find the chance of hitting the shaded area by finding the ratio shaded area / total area. (use the approximation π ≈ 3.1416, as needed. assume that each point on the target is equally likely to be hit.) the chance of hitting the shaded region is 0.106 %. (round to the nearest whole number as needed.)

Explanation:

Step1: Calculate total area

The total area of the target is the area of the out - most circle with radius $r_{total}=\frac{24}{2}=12$ inches. Using the formula for the area of a circle $A = \pi r^{2}$, we have $A_{total}=\pi\times(12)^{2}=144\pi$ square inches.

Step2: Calculate the area of non - shaded parts

The non - shaded inner circle has radius $r_1=\frac{14}{2} = 7$ inches, so its area $A_1=\pi\times(7)^{2}=49\pi$ square inches. The next non - shaded circle has radius $r_2=\frac{12}{2}=6$ inches, so its area $A_2=\pi\times(6)^{2}=36\pi$ square inches.

Step3: Calculate shaded area

The shaded area $A_{shaded}=A_{total}-A_1 - A_2=144\pi-49\pi - 36\pi=(144 - 49 - 36)\pi=59\pi$ square inches.

Step4: Calculate the ratio

The ratio of the shaded area to the total area is $\frac{A_{shaded}}{A_{total}}=\frac{59\pi}{144\pi}=\frac{59}{144}\approx0.4097$. To convert this to a percentage, we multiply by 100: $0.4097\times100 = 40.97\%\approx41\%$.

Answer:

$41\%$