Question

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%

Answer 1

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

$A_c=\pi \left(\dfrac{a}{2}\right)^2=\dfrac{22}{7}\times\dfrac{a^2}{4}=\dfrac{11}{14}a^2.$

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

$A_{ns}=A_s-A_c=a^2-\dfrac{11}{14}a^2=\dfrac{3}{14}a^2.$

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

$p=\dfrac{A_{ns}}{A_s}\times100\%=\dfrac{\frac{3}{14}a^2}{a^2}\times100\%=\dfrac{300}{14}\%=21.42\%(approx.)$

Thus, the required probability is 20%.

Option (C) is CORRECT.

Answer 2

Answer:

i think so 5%

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Step-by-step explanation: