Question

Geometric Probability
Acellus
Find the probability that a
randomly selected point within the
circle falls in the red shaded area.
r = 4 cm
p = [?]
Enter a decimal rounded to the nearest hundredth.
Enter

Answer 1

Answer:

The probability is 0.32

Step-by-step explanation:

we know that

The probability that a  randomly selected point within the  circle falls in the red shaded area is equal to divide the area of the red shaded area by the area of the circle

step 1

Find the area of the circle

$A=\pi r^{2}$

we have

$r=4\ cm\\\pi=3.14$

substitute

$A=(3.14)(4)^{2}=50.24\ cm^2$

step 2

Find the area of the red shaded area (triangle)

The area of red triangle is

$A=\frac{1}{2}(b)(h)$

we have

$b=2r=2(4)=8\ cm\\h=r=4\ cm$

substitute

$A=\frac{1}{2}(8)(4)=16\ cm^2$

step 3

Find the probability

$\frac{16}{50.24}= 0.32$