area of a circular field is154 sq.m. find the time taken byan athlete to complete 2 rounds if the speed is 5 km per hour?

Then area of circular field = ${\mathrm{\pi r}}^{2}=154{\mathrm{m}}^{2}$

$\Rightarrow \frac{22}{7}{r}^{2}=154\phantom{\rule{0ex}{0ex}}\Rightarrow {r}^{2}=\frac{7}{22}\times 154\phantom{\rule{0ex}{0ex}}\Rightarrow {r}^{2}=49\phantom{\rule{0ex}{0ex}}\Rightarrow r=\sqrt{49}=7$

Then circumference of circular field = $2\mathrm{\pi r}=2\times \frac{22}{7}\times 7=44$ m

So distance of one round of circular field = circumference of circular field = 44 m

Then distance of 2 round of circular field = $44\times 2$ = 88 m

Speed = 5 km/hr = $\frac{5\times 1000}{60\times 60}=\frac{25}{18}\mathrm{m}/\mathrm{s}$

Therefore time taken to cover 2 round of circular field = $\frac{88}{{\displaystyle \frac{25}{18}}}=\frac{88\times 18}{25}=63.36\mathrm{seconds}$

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