This-is-a-simple-question-but-for-some-silly-reason-I-can-t-figure-it-out-1-If-I-have-a-circle-with-radius-r-and-area-A-and-I-wish-to-make-a-new-circle-with-n-times-the-area-for-what-new-value-

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Question Number 4496 by FilupSmith last updated on 01/Feb/16

$$\mathrm{This}\mathrm{is}\mathrm{a}\mathrm{simple}\mathrm{question}\mathrm{but}\mathrm{for}\mathrm{some}$$$$\mathrm{silly}\mathrm{reason}\mathrm{I}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{figure}\mathrm{it}\mathrm{out}\dots$$$$$$$$1.$$$$\mathrm{If}\mathrm{I}\mathrm{have}\mathrm{a}\mathrm{circle}\mathrm{with}\mathrm{radius}r\mathrm{and}$$$$\mathrm{area}A,\mathrm{and}\mathrm{I}\mathrm{wish}\mathrm{to}\mathrm{make}\mathrm{a}\mathrm{new}\mathrm{circle}\mathrm{with}$$$$n\mathrm{times}\mathrm{the}\mathrm{area},\mathrm{for}\mathrm{what}\mathrm{new}\mathrm{value}$$$$\mathrm{of}r\mathrm{should}\mathrm{be}\mathrm{used}?$$$$$$$$2.$$$$\mathrm{What}\mathrm{if}\mathrm{I}\mathrm{increase}\mathrm{the}\mathrm{area}\mathrm{from}A\mathrm{to}$$$$A+n?\mathrm{What}\mathrm{value}\mathrm{of}r\mathrm{would}\mathrm{be}\mathrm{used}\mathrm{here}?$$

Commented by prakash jain last updated on 01/Feb/16

$$A_1=\pi r_1^2=nA=n\pi r^2\Rightarrow r_1=r\sqrt{n}$$$$A_1=\pi r_1^2=A+n=\pi r^2+n\Rightarrow r_1=\sqrt{r^2+\frac{n}{\pi }}$$

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