A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Question

anonymous · Answer

https://chcs4237-cchsgpe-ccl.gradpoint.com/Resource/4990673,8A6,0,0,0,0,0/Assets/testitemimages/geometry_b/area/mc134-1.jpg

cwrw238 · Answer

you need to find what fraction of the square is occupied by the 4 circles
probability = area circles / total area of square;

if you let each side of the square be  4a units
then the radius of each circle will be a units

cwrw238 · Answer

its now easy to work out the 2 areas

cwrw238 · Answer

area of 4 circles = 4 * pi a^2
total area = 4a 4a  = 16a^2

required probability = 4 pi a^2
                                   -------
                                      16 a^2

cwrw238 · Answer

simplify that and you have the answer

cwrw238 · Answer

you can leave your answer in terms of pi or write ir as a decimal correct to , say, 3 places