Question

If Raj randomly chooses a point in the square below, what is the probability that point is not in the circle? Assume that pi = 3.14 and round to the nearest tenth of a percent. A circle inside of a square. The radius of the circle is 4 units. The side of the square is 10 units.

Answer 1

49.7%

Explanation:

A cdircle is located within a square.

Area of the circle

Area =
`\pi`
`r^(2)`, where r = 4 units.

Area Circle = 50.3 units^2

Area of the square

Area = l*w or l^2 for a square, since l = w

Area = (10 units)^2

Area = 100 units^2

Area in the square but outside the circle

This is the difference [Square minus Circle Areas]

Square minus Circle Areas = 100 - 50.3 or 49.7 units^2

Probability

The probability of picking a point in the square that is not in the circle is the ration of the two areas: [Outside Circle/Square]x100%

(49.7 units^2)/(100 units^2)x100% = 49.7%