SOLUTION: What is the maximum area that can be enclosed by a wire of length 24 cm by bending it in the form of a sector of the circle ? Thank you sir.

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Question 893080: What is the maximum area that can be enclosed by a wire of length 24 cm by bending it in the form of a sector of the circle ?
Thank you sir.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
What is the maximum area that can be enclosed by a wire of length 24 cm by bending it in the form of a sector of the circle ?
:
let a = arc distance of the sector
let r = radius of the circle
then
a + 2r = 24
a = (24-2r)
:
Find the portion of the circle in the sector (arc/circumference)
a%2F%282pi%2Ar%29
Replace a with (24-2r)
%28%2824-2r%29%29%2F%282%2Api%2Ar%29
simplifies to
%28%2812-r%29%29%2F%28pi%2Ar%29
Find the area of the sector
A = %28%2812-r%29%29%2F%28pi%2Ar%29 * pi%2Ar%5E2
Cancel pi*r
A = (12-r) * r
A = -r^2 + 12r
Max of this quadratic equation occurs at the axis of symmetry; x=-b/(2a)
r = %28-12%29%2F%282%2A-1%29
r = 6 cm
Find the max area
A = -6^2 + 12(6)
A = -36 + 72
A = 36 sq cm max area