Question

The circle below has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters.
What is the probability that a point chosen at random is in the blue region?
155
155
Mark this and return
Save and Exit
Save and Exit
has
submit

Answer 1

Answer:

77.5%

Step-by-step explanation:

see the attached figure to better understand the problem    

step 1

Find the radius of the circle

The area of the circle is

$A=\pi r^{2}$

we have

$A=314\ cm^2$

assume

$\pi =3.14$

substitute and solve for r

$314=(3.14)r^{2}$

$r^{2}=314/(3.14)$

$r^{2}=100$

$r=10\ cm$

step 2

Find the area of the square outside the circle

The length side of the square is the diameter of the circle

$D=2(10)=20\ cm$

$A=20^{2}=400\ cm^2$

step 3

Determine the area of the blue region

The area of the blue region is the area of circle minus the area of the square inside the circle

$A=314-2^2=310/ cm^2$

step 4

The probability that a point chosen at random is in the blue region is equal to divide the area of the blue region by the total area of the outside square

310/400

simplify

31/40=0.775

Convert to percentage

0.775*100=77.5%

Answer 2

Answer:

Lets get this right, it is D. 155/157

Step-by-step explanation:

Area of square is 4, area of circle is 314. To find area of blue do 314-4. To find area you get 310/314. Simplify by dividing both by 2, you get 155/157.