গোলাকার ৪০০ মিটার মাঠে একজন দৌড়বিদ ২৪ চক্কর দৌড়ালে, সে কত কিলোমিটার দূরত্ব অতিক্রম করবে?

বৃত্তের দৈর্ঘ্যকে পরিধি বলা হয় ।

$$\begin{gathered} Let us depict a figure according to question \\ Here, ABCD is a 3 by 4 rec\tan gle which is inscribed in a circle. \\ \therefore Diagonal of the rectangle area, AC=D^{\sqrt{A{D}^2+C{D}^2}}=C^{\sqrt{3^2+4^2}}=\sqrt{9+16}=\sqrt{25}=5 unit \end{gathered}$$

$$\begin{gathered} \therefore Radius of the circle =\frac{5}{2} unit \\ \therefore Circumference of the circle = 2\pi r [Here, r = radius] \\ =2\times 3.1416 \times \frac{5}{2}=15.71 unit. \end{gathered}$$

Let, Radius of the garden with road is = R meter

& Radius of the garden without road is = r meter

$\therefore$Outer circumstance of the garden 2πR meter

$\therefore$Inner circumstance of the garden 2πr meter

Here, width of the road (R-r) meter

According to question,

2πR - 2πr = 88

= (R - r) $\times$ 2π= 88

$\therefore$R-r=$\frac{88}{2\mathrm{\pi }}=\frac{88}{{\displaystyle \frac{2\times 22}{7}}}=\frac{88}{1}\times \frac{7}{2\times 22}=14 meters$

$\therefore$Width of the road is 14 meters.

2πr

পাই ($\mathrm{\pi }$) এর মান = $\frac{২২}{৭}=৩.১৪১৬$

$2 \pi r$