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What is the probability that the dart will land in the shaded(black) area?

 

Picture: 

Oops, not a good drawer. LOL! Imagine this, but the circle is cut in fourths, and two pieces are shaded black. https://www.google.com/search?q=circle+inscribed+in+a+square&safe=active&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiltpGloIXfAhWEdN8KHZjOBbIQ_AUIDigB&biw=1600&bih=789#imgrc=nTA5tZW-9cTF_M:

 Dec 4, 2018
 #1
avatar+100439 
+2

If the circle is inscribed in the square....let the side of the square = S...so...its area = S^2

The radius of the circle is S/2

So....the area of the circle is pi (S/2)^2 =  (pi/4)S^2

And the black area is (1/2) of this =  (pi/8)S^2

 

So....P(hitting the black area)  =   Black Area / Total Area of Square =

 

(pi/ 8)S^2              pi / 8   ≈   .3927 =   39.27%  

________  = 

      S^2

 

 

cool cool cool

 Dec 4, 2018
 #2
avatar+866 
+1

Thanks, CPhill! You can also label the radius of the circle, and find from that!

ant101  Dec 4, 2018

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