A rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 500 meters. Answer the following:a) Express the area of the rectangular field (shaded green) in terms of r
a) area of whole- area of circle
500=2x+2pir
500-2pir=2x
250-pir=x
pir^2 + 2rx - pir^2
pir^2-2(250-pir)-pir^2
-500-2pir=A(r)
b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
Maximum area = square meters
*I cant seem to get the area equation right so I cant finish part b.. or even start!
a) area of whole- area of circle
500=2x+2pir
500-2pir=2x
250-pir=x
pir^2 + 2rx - pir^2
pir^2-2(250-pir)-pir^2
-500-2pir=A(r)
b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
Maximum area = square meters
*I cant seem to get the area equation right so I cant finish part b.. or even start!
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