Question

A target with a diameter of 70 cm has 4 scoring zones formed by concentriccircles. The diameter of the center circle is 10 cm. The width of each ring is 10cm. A dart hits the target at a random point. Find the probability that it will hit apoint in the yellow region.

Answer 1

The probability is equal to divide the area of the yellow region by the area of the complete circle

so

step 1

Find the area of teh complete circle

r=70/2=35 cm

substitute

`\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ cm2} \end{gathered}`

step 2

Find the area of the yellow region

`\begin{gathered} A=\pi(35^2-25^2) \\ A=600\pi\text{ cm2} \end{gathered}`

step 3

find the probability

P=600pi/1,225pi

P=0.4898

or

P=48.98%