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

Step-by-step 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=$\frac{d}{2}=\frac{124}{2}=62\ m$

Area of circle=$\pi\ r^2=3.14\times(62)^2=3.14\times3.14=12,070.16\ m^2$

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

$=\frac{\text{area of shaded region}}{\text{area of square}}=\frac{3305.84}{15376}=0.215$