The circle below has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. A circle is shaded blue. A small unshaded square is at the center of the circle.

31/40

Step-by-step explanation:

The question is incomplete. Here is the complete question with appropriate diagram.

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?

Given the area of the circle to be 314cm², we need to get the diameter of the circle first since the diameter of the circle is equivalent to length of the side of the square inscribed in it.

Using the formula Area of a circle = πr²

314 = 3.14r²

r² = 314/3.14

r² = 100

r = 10 cm

Diameter of the circle = 2*10 = 20 cm

Area of a square = Length * length

Area of the outer square = 20*20 = 400cm²

Area of the inner square with side length 2cm = 2*2 =4cm²

Area of the shaded region = Area of the square - Area of the inner square

= 314-4 = 310cm²

The probability that a point chosen at random is in the blue region = Area of the shaded region/total area of the outer square

= 310/400

= 31/40

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