Question

Need an answer quick. If a circle with a diameter of 124 m is inscribed in a square, what is the probability that a point picked at random in the square is in the shaded region? Round to the nearest thousandth.

A.
0.013
B.
0.032
C.
0.215
D.
0.785

Answer 1

Answer: C. 0.215

Explanation:

Given: A circle with a diameter of 124 m is inscribed in a square .

Thus side of square =124 m

Now, area of square=
`(side)^2=(124)^2=15,376\ m^2`

Radius of circle=
`(d)/(2)=(124)/(2)=62\ m`

Area of circle=
`\pi\ r^2=3.14*(62)^2=3.14*3.14=12,070.16\ m^2`

Now, Area of shaded region= Area of square-Area of circle

Area of shaded region=
`15,376-12,070.16=3,305.84\ m^2`

Probability that a point picked at random in the square is in the shaded region

`=\frac{\text{area of shaded region}}{\text{area of square}}=(3305.84)/(15376)=0.215`