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 ? 
:
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/(2pi*r)}}}
Replace a with (24-2r)
{{{((24-2r))/(2*pi*r)}}}
simplifies to
{{{((12-r))/(pi*r)}}}
Find the area of the sector
A = {{{((12-r))/(pi*r)}}} * {{{pi*r^2}}}
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 = {{{(-12)/(2*-1)}}}
r = 6 cm
Find the max area
A = -6^2 + 12(6)
A = -36 + 72
A = 36 sq cm max area