Question

The sides of a square field are 32 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.

Answer 1

You find the area not touched by the sprinkler by subtracting the area of the circle from the area of the square.  The area of the square is 32*32 which is 1024.  The area of the circle is found by multiplying 3.14 by the radius squared.  Our radius is half the diameter of 32, so r = 16.  A=3.14(16)(16) which gives us an area of the circle to be 803.84.  Subtracting the 2 areas, square minus circle, is 1024-803.84=220.16 meters squared.