Twenty four meters of wire is available to fence off a flower bed in the form of a circular sector.
Twenty four 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?
Answer/Solution
6
Steps/Work
Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 24
=> x/360*2*pi*r +2r= 24
=> 2A/r+2r=24
=> A= r12-r^2
= r12-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 12-2r=0
r=6
C
Circumference of the sector = 24
=> x/360*2*pi*r +2r= 24
=> 2A/r+2r=24
=> A= r12-r^2
= r12-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 12-2r=0
r=6
C