Q:

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.0.013B.0.032C.0.215D.0.785

Accepted Solution

A:
Answer: C. Β 0.215
Step-by-step explanation:Given: A circle with a diameter of 124 m is inscribed in a square .Thus side of square =124 mNow, area of square=[tex](side)^2=(124)^2=15,376\ m^2[/tex]Radius of circle=[tex]\frac{d}{2}=\frac{124}{2}=62\ m[/tex]Area of circle=[tex]\pi\ r^2=3.14\times(62)^2=3.14\times3.14=12,070.16\ m^2[/tex]Now, Area of shaded region= Area of square-Area of circleArea of shaded region=[tex]15,376-12,070.16=3,305.84\ m^2[/tex]Probability that a point picked at random in the square is in the shaded region[tex]=\frac{\text{area of shaded region}}{\text{area of square}}=\frac{3305.84}{15376}=0.215[/tex]