Sophia throws a dart at this square-shaped target:

A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3.

Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work.

Respuesta :

Answer:

Area of square = x² (where x is the measure of a side)

Given x = 9:

⇒ area of square = 9² = 81 square units

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Area of a circle = [tex]\pi[/tex]r² (where r is the radius of the circle)

Given diameter = 3

⇒ radius = 3 ÷ 2 = 1.5

⇒ area of circle = [tex]\pi[/tex] × 1.5²

                          = 2.25[tex]\pi[/tex]

                          = 7.068583471... square units

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Area of portion between edge of square and edge of circle

= area of square - area of circle

= 81 - 2.25[tex]\pi[/tex] = 73.93141653... square units

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Probability of hitting the circle = 2.25[tex]\pi[/tex] / 81

                                                  = 0.0872664626

⇒ Closer to zero

Probability of hitting the area outside the circle = 73.93141653... / 81

                                                                              = 0.9127335374...

⇒ Closer to 1

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**I don't know which part of the target is the white portion, so I have given answers for both areas**