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The circle has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. What is the probabili

Home/Math/The circle has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. What is the probabili

The circle has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. What is the probabili

Question

The circle 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?

see the attached figure to better understand the problem

step 1

Find the radius of the circle

The area of the circle is

we have

assume

substitute and solve for r

step 2

Find the area of the square outside the circle

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

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

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

## Answers ( )

Step-by-step explanation: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

we have

assume

substitute and solve for r

step 2

Find the area of the square outside the circle

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

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

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%…

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