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Question Number 215193 by MATHEMATICSAM last updated on 31/Dec/24

Commented by MATHEMATICSAM last updated on 31/Dec/24

$$\mathrm{If}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{smaller}\mathrm{circle}\mathrm{is}a\mathrm{sq}\mathrm{unit}$$$$\mathrm{and}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{larger}\mathrm{circle}\mathrm{is}A\mathrm{sq}\mathrm{unit}$$$$\mathrm{find}\frac{a}{A}.$$

Answered by som(math1967) last updated on 31/Dec/24

$$letsideofsquare=x$$$$\therefore a=\frac{\pi x^2}{4}$$$$A=\pi {\left(\frac{x\sqrt{2}}{2}\right)}^2=\frac{\pi x^2}{2}$$$$\frac{a}{A}=\frac{\pi x^2}{4}\times \frac{2}{\pi x^2}=\frac{1}{2}$$$$$$

Answered by mr W last updated on 02/Jan/25

$${it}^{\prime }sclear\frac{r}{R}=\frac{1}{\sqrt{2}},therefore$$$$\frac{a}{A}={\left(\frac{r}{R}\right)}^2=\frac{1}{2}$$

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