Circle is inscribed in a square with a side length of 4. If a point in the square is chosen at random, what is the probability that the point is in the square but not in the circle? Express your answer as a percent, and round to the nearest tenth.

Step-by-step explanation:

The formula for determining the area of a square is expressed as

Area = Length²

Length of square 4

Area of square = 4² = 16

Since the circle is inscribed in the square, its diameter = 4

Radius = diameter/2 = 4/2 = 2

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

Area of circle = 3.14 × 2² = 12.56

Area inside the square but outside the circle is

16 - 12.56 = 3.44

Probability is expressed as

Number of favourable outcome/number of total outcome

Therefore, probability that the point is in the square but not in the circle is

3.44/16 = 0.215

Converting to percentage, it becomes

0.215 × 100 = 21.5%

89

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