Question

A square is inscribed in a circle with a radius of "72".If a point in the circle is chosen at random, what is the probability that the point is outside the square?

round your answer to the nearest tenth of a percent

Answer 1

36.3%

Explanation:

If a square is inscribed in a circle, the diagonals of the square must pass through the center of the circle and be equal to the diameter

Radius of circle = 72

Diameter of circle = 72 x 2 = 144

Therefore the diagonal of the square:

d = 144

If the side of a square is a, the diagonal is given by the formula

d = a√2

Plugging in the known value of d = 144 we get
a√2 = 144

a = 144/√2

Area of the square = a² = (144/√2)² = 144²/2 = 10,368

Area of the circle = πr² = (72)² x π = 16,286 rounded to nearest integer

Area of region outside the square = 16,286 - 10, 368 = 5,918

P(point outside square) = Area of region outside square/area of circle

= 5,918/16,286

= 0.3634

= 36.34 %

= 36.3 % rounded to the nearest tenth