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Question Number 5556 by Rasheed Soomro last updated on 20/May/16

$$\mathrm{The}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{is}\mathrm{diretly}$$$$\mathrm{proportional}\mathrm{to}\mathrm{the}\mathrm{square}\mathrm{of}$$$$\mathrm{its}\mathrm{diameter}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{constant}\mathrm{of}\mathrm{proportionality}?$$

Commented by Yozzii last updated on 20/May/16

$$A\propto d^2$$$$A=k{\left(2r\right)}^2(d=2r>0)$$$$\pi r^2=4{kr}^2$$$$\Rightarrow k=\frac{\pi }{4}.$$$$Alternatively,sinceA=\frac{\pi }{4}{d}^2$$$$\Rightarrow A\propto d^2\Rightarrow k=\pi /4$$

Commented by Rasheed Soomro last updated on 20/May/16

$$\mathrm{Your}\mathrm{way}\mathrm{is}\mathrm{better}\mathrm{than}\mathrm{the}\mathrm{way}$$$$\mathrm{I}\mathrm{saw}\mathrm{in}\mathrm{a}\mathrm{book}!$$

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