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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. $\endgroup$
    – Harambe
    Apr 5, 2017 at 9:48
  • $\begingroup$ an edit is suggested @Sanjay Bhatnagar $\endgroup$
    – Pole_Star
    Apr 10, 2017 at 5:15

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