Question

The shaded portion in the figure given below 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 m²
• B. 754.5 m²
• C. 854.5 m²
• D. 554.5 m²

Answer 1

The correct option is A

654.5 m²

Let the radius of the inner circle be r m

Therefore, $2\pi r=176\Rightarrow 2\times \frac{22}{7}\times r=176m$

$\Rightarrow r=176\times \frac{7}{2\times 22}m=28m$

Since, the width of the path = 3.5 m

The 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 = 654.5 $m^2$