20 meters of wire is available for fencing off a flower-bed in the form of a circular sector.
Then what is the maximum area (in sq. m) of the flower-bed?
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This is a very simple question. Let $M$ be the angle, the arc of the sector $AOB$ makes with the center $O$. Let OA = OB = radius r.
Given $$ OA + arc AB + OB = 20 $$ $$2r + rM = 20 $$ $$ M = {20-2r}{r}$$
Area $A$ of the sector =$ \frac{M}{2}r^2 = 10r-r^2$
$$\frac{dA}{dr}= 10 - 2r = 0$$ $$r=5$$
Second derivative is negative for $r =5$
We get maximum area at $r=5$
$A = 25 $
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$\begingroup$ can you tidy up the maths typesetting? It's quite difficult to follow. $\endgroup$– HarambeApr 5, 2017 at 9:48
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