32 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 32 = > x / 360 * 2 * pi * r + 2 r = 32 = > 2 a / r + 2 r = 32 = > a = r 16 - r ^ 2 = r 16 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 16 - 2 r = 0 r = 8 e
divide(32, const_4)