Question

If a point is chosen inside the square, what is the probability that it will also be inside the circle?

Answer 1

Answer:

$79\%$

Step-by-step explanation:

The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.

Formulas used:

• Area of a square with side length $s$ is given by $A=s^2$
• Area of a circle with radius $r$ is given by $A=r^2\pi$

The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:

Area of square: $A=2^2=4$

Area of circle:

$A=1^2\pi=\pi$

Therefore, the probability that the point will be inside the circle is:

$\frac{\pi}{4}=0.78539816339\approx \boxed{79\%}$