Question

12. What is the probability that a point in the square below
is in the shaded region? Write your answer as a
percent.

Answer 1

Answer:

$21.5\%$

Step-by-step explanation:

we know that

The probability that a point in the square below  is in the shaded region, is equal to divide the area of the shaded region by the area of the square

step 1

Find the area of the shaded region

The area is equal to the area of the square minus the area of the circle

$A=b^{2} -\pi(r)^{2}$

we have

$b=12\ cm$ ---> length side of the square

$r=12/2=6\ cm$ ----> the radius is half the diameter

assume

$\pi =3.14$

substitute

$A=12^{2} -(3.14)(6)^{2}$

$A=30.96\ cm^{2}$

step 2

Find the area of the square

$A=b^{2}$

we have

$b=12\ cm$ ---> length side of the square

substitute

$A=12^{2}=144\ cm^{2}$

step 3

Find the probability

$P=30.96/144=0.215$

Convert to percent form

$0.215*100=21.5\%$