Question

If a dart hits the target at random, what is the probability that it will land in the shaded region. A. 1/4B. 1/16πC. 1/16D. 16π

Answer 1

step 1

Find out the area of the complete circle

`A=pi*r^2`

where

r=12 in

`\begin{gathered} A=pi*12^2 \\ A=144pi\text{ in}^2 \end{gathered}`

step 2

Find out the area of the shaded region

r=3 in

`\begin{gathered} A=pi*3^2 \\ A=9pi\text{ in}^2 \end{gathered}`

The probability is equal to dividing the area of the shaded region by the area of the complete circle

so

`P=(9pi)/(144pi)=(9)/(144)=(1)/(16)`

The answer is option C