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Question Number 43992 by ajfour last updated on 19/Sep/18

Commented by ajfour last updated on 19/Sep/18

If square has as much area   outside circle as circle has  outside square, relate a, and R.

$${If}\:{square}\:{has}\:{as}\:{much}\:{area}\: \\ $$$${outside}\:{circle}\:{as}\:{circle}\:{has} \\ $$$${outside}\:{square},\:{relate}\:\boldsymbol{{a}},\:{and}\:\boldsymbol{{R}}. \\ $$

Answered by MrW3 last updated on 19/Sep/18

πR^2 =a^2   ⇒(a/R)=(√π)

$$\pi{R}^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$$$\Rightarrow\frac{{a}}{{R}}=\sqrt{\pi} \\ $$

Commented by math1967 last updated on 20/Sep/18

why area of circle=area of square sir?

$${why}\:{area}\:{of}\:{circle}={area}\:{of}\:{square}\:{sir}? \\ $$

Commented by MrW3 last updated on 20/Sep/18

Commented by MrW3 last updated on 20/Sep/18

Area of square=shaded+blue  Area of circle=shaded+yellow  since blue=^(!) yellow,  ⇒square=circle

$${Area}\:{of}\:{square}={shaded}+{blue} \\ $$$${Area}\:{of}\:{circle}={shaded}+{yellow} \\ $$$${since}\:{blue}\overset{!} {=}{yellow}, \\ $$$$\Rightarrow{square}={circle} \\ $$

Commented by ajfour last updated on 20/Sep/18

common area+circular segment  areas= common area+corner  segment areas  ⇒   πR^2  = a^2     (obviously).

$${common}\:{area}+{circular}\:{segment} \\ $$$${areas}=\:{common}\:{area}+{corner} \\ $$$${segment}\:{areas} \\ $$$$\Rightarrow\:\:\:\pi{R}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:\:\:\:\left({obviously}\right). \\ $$

Commented by math1967 last updated on 20/Sep/18

OK sir,thank you

$${OK}\:{sir},{thank}\:{you} \\ $$

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