Question

"If a dart hits the target at random, what is the probability that it will land in the shaded region?

Answer 1

Answer: $P=\frac{1}{16}$

Step-by-step explanation:

In the given picture, the the radius of the shaded region = 3 inches

The area of the shaded region =$\pi r^2=3.14\times(3)^2=3.14\times9$

Thus, The area of the shaded region =28.26 square inches

Radius of whole figure = 12 inches

The area of whole figure= $\pi r^2=3.14\times(12)^2=3.14\times144$

Thus, The area of the whole figure=452.16 square inches

Now, the probability that it will land in the shaded region is given by :-

$P=\frac{\text{area of shaded region}}{\text{area of the whole figure}}\\\\\Rightarrow\ P=\frac{28.26}{452.16 }\\\\\Rightarrow\ P=\frac{1}{16}$

Answer 2

1) circle area = $\pi r^{2}$
2) whole circle area = 12^2 $\pi$  = 144 $\pi$
3) shaded area = 3^2 $\pi$ = 9 $\pi$
4) probability 

= $\frac{9 \pi }{144 \pi }$
simplify to 
$\frac{1}{16}$

answer C