Question

In a battle, the commander-in-chief arranges his soldiers in a formation of three concentric circles. The radii of the circles are in an arithmetic progression: the smallest radius is $70	ext{ m}$ (meters) and the largest is $140	ext{ m}$. If each soldier is to be separated from the adjacent soldiers standing on the same circle by $1	ext{ m}$, how many soldiers are required to complete the formation? (Consider $\pi = 22/7$.)

Accepted Answer

D. Let the three concentric circles be $C_1, C_2, C_3$ with radii $r_1, r_2, r_3$. Given $r_1 = 70	ext{ m}$ and $r_3 = 140	ext{ m}$, and since $r_1, r_2, r_3$ are in AP, $r_2 = \frac{70 + 140}{2} = 105	ext{ m}$. The total perimeter of all three circles is: $$	ext{Total Circumference} = 2\pi(r_1 + r_2 + r_3) = 2 	imes \frac{22}{7} 	imes (70 + 105 + 140) = 2 	imes \frac{22}{7} 	imes 315 = 1980	ext{ m}$$ Since soldiers are separated by $1	ext{ m}$ on each circumference, the number of soldiers required is $1980$.

Soldiers in concentric circles

Explanation

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