Four hundred meter of fencing are required to enclose a square field .what area can be enclosed by the same length of fencing if the enclosure is circular?

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Four hundred meter of fencing are required to enclose a square field .what area can be enclosed by the same length of fencing if the enclosure is circular?

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Answer 1 · 2018-05-01T05:09:05

$= \frac{40000}{π} m^{2}$ $= 40000/pi m^2$
$\approx 12732.395 m^{2}$ $~~12732.395 m^2$

Explanation:

The length of the fencing is $400 m$ $400m$ . So we must find the area of a circle with circumference $\approx 400 m$ $~~ 400m$ . Note that due to the transcendental nature of $π$ $pi$ , the exact value cannot be calculated.
$2 π r = 400$ $2pir = 400$
$\Rightarrow r = \frac{200}{π}$ $implies r = 200/pi$

Area of a circle equals $π r^{2}$ $pir^2$
$= π {(\frac{200}{π})}^{2}$ $= pi(200/pi)^2$
$= π \frac{40000}{π^{2}}$ $= pi(40000)/pi^2$
$= \frac{40000}{π} m^{2}$ $= 40000/pi m^2$
$\approx 12732.395 m^{2}$ $~~12732.395 m^2$

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Four hundred meter of fencing are required to enclose a square field .what area can be enclosed by the same length of fencing if the enclosure is circular?

1 Answer

Explanation:

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