A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded. A.25% B.10% C.20% D.5…

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asked Jan 28, 2020 196k views

2 Answers

CBGraham · Answer 1 · 2020-02-02T13:37:12+0000

Answer: The correct option is (C) 20%.

Step-by-step explanation: Given that a circle is inscribed in a square and a point in the figure is selected at random.

We are to find the probability that the point will lie in the part that is NOT shaded.

Let a units be the side length of the square.

Then, the area of the square will be

A_s=a^2.

Also, the radius of the circle is equal to the half of the side length of the square. So, the area of the circle will be

$A_c=\pi \left((a)/(2)\right)^2=(22)/(7)*(a^2)/(4)=(11)/(14)a^2.$

So, the area of the part that is not shaded is given by

A_(ns)=A_s-A_c=a^2-(11)/(14)a^2=(3)/(14)a^2.

Therefore, the probability that the selected point is not in the shaded part is given by

$p=(A_(ns))/(A_s)*100\%=((3)/(14)a^2)/(a^2)*100\%=(300)/(14)\%=21.42\%(approx.)$

Thus, the required probability is 20%.

Option (C) is CORRECT.