Question

A battle commander arranged his soldiers in three concentric circles. The inner radius is 70 m and the outer radius is 140 m. If the distance between any two adjacent soldiers on each circle is 1 m, how many total soldiers are required?

• A. 1320
• B. 1980
• C. 2640
• D. 3960

Hint:

When objects are placed uniformly on a circle, their count is equal to the circumference divided by spacing.

Answer 1

The Correct Option is B

Step 1: Identify the radii of the three circles.
Since the circles are concentric and equally spaced, the radii are:
Inner circle \( r_1 = 70 \) m
Middle circle \( r_2 = 105 \) m
Outer circle \( r_3 = 140 \) m
Step 2: Find circumference of each circle.
Circumference \( = 2\pi r \)
\[ C_1 = 2\pi \times 70 = 140\pi \] \[ C_2 = 2\pi \times 105 = 210\pi \] \[ C_3 = 2\pi \times 140 = 280\pi \]
Step 3: Convert circumference into number of soldiers.
Distance between adjacent soldiers is 1 m, so number of soldiers equals circumference.
\[ \text{Total soldiers} = 140\pi + 210\pi + 280\pi = 630\pi \]
Step 4: Calculate numerical value.
Using \( \pi = \frac{22}{7} \):
\[ 630 \times \frac{22}{7} = 1980 \]
Final Answer:
\[ \boxed{1980} \]