Question

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

A. 1/4
B. 1/16[pi]
C. 1/16
D. 16[pi]"

Answer 1

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

=
`(9 \pi )/(144 \pi )`
simplify to

`(1)/(16)`

answer C

Answer 2

Answer:
`P=(1)/(16)`

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*(3)^2=3.14*9`

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*(12)^2=3.14*144`

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=(28.26)/(452.16 )\\\\\Rightarrow\ P=(1)/(16)`