Question

A man runs with the speed of 15.84 km. hr. He completes 12 rounds of a circular ground in our hour, find the area of the ground in sq. m.

Answer 1

Distance covered in 1 h = 15.84 km = 15840 m
In 1 h, he takes 12 rounds.
i.e., Distance covered in 12 rounds = 15840 m

$\therefore$ Distance covered in one round = $\frac{15840}{12}$ m = 1320 m

Let the radius of the ground be r m.
Now, distance covered in one round = circumference of the ground
$\Rightarrow$ 1320 =2$\pi$r
$$\begin{gathered} \Rightarrow 1320=2\times \frac{22}{7}\times r \\ \Rightarrow \frac{1320\times 7}{2\times 22}=r \\ \Rightarrow r=210\mathrm{m} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{ground}=\pi r^2 \\ =\frac{22}{7}\times 210\times 210 \\ =138600{\mathrm{m}}^2 \end{gathered}$$