Question

The shaded portion in the adjoining figure shows a circular path enclosed by two concentric circles. If the inner circumference of the path is 176 m and the uniform width of the circular path is 3.5 m, find the area of the path.

• A. 654.5 $m^2$​
• B. 754.5 $m^2$​
• C. 854.5 $m^2$​
• D. 554.5 $m^2$​

Answer 1

The correct option is A 654.5 $m^2$​

Let the radius of the inner circle be r.
$\Rightarrow 2\pi r=176m\Rightarrow 2\times \frac{22}{7}\times r=176$
$\Rightarrow r=176\times \frac{7}{2\times 22}=28m$

Since, the width of the path = 3.5 m,
radius of the outer circle (R) = r + 3.5 m = 28 m + 3.5 m = 31.5 m

The area of the circular path
= Area of the outer circle – Area of the inner circle
$=\pi R^2–\pi r^2$
$=(\frac{22}{7}\times 31.5\times 31.5)–(\frac{22}{7}\times 28\times 28)=3118.5–2464=654.5m^2$