Question

A circle is inscribed in a square with a side length of 180. If a point in the square is chosen at

random, what is the probability that the point is inside the circle?
Round your answer to the nearest tenth of a percent.
%

Answer 1

The area of the circle is approximately 25447.2 square units.

The probability that the point is inside the circle is approximately 78.5%.

Step-by-step explanation:

To find the probability that a randomly chosen point in the square is inside the inscribed circle, we need to compare the areas of the circle and the square.

The area of the square is 180^2 = 32400 square units.

The area of the circle is πr^2, where r is the radius of the circle. Since the square's side length is 180, the diameter of the circle is also 180, so the radius is 90.

Now we can calculate the area of the circle:

π(90^2) ≈ 25447.2 square units.

To find the probability, we divide the area of the circle by the area of the square:

25447.2 / 32400 ≈ 0.785 (rounded to three decimal places).

Finally, we convert the decimal to a percentage: 0.785 * 100 = 78.5% (rounded to the nearest tenth of a percent).