The shaded portion in the below 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."

Given:

The inner circumference of the path is 176 m and the uniform width of the circular path is 3.5 m.

To do:

We have to find the area of the path.

Solution:

Let the radius of the inner circle be $r$ and the width enclosed by the two circles be $w$.

We know that,

Circumference of a circle of radius $r=2\pi r$.

Circuference of the inner circle $=176\ m$

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

$r=\frac{176\times7}{44}$

$r=4\times7$

$r=28\ m$

Radius of the outer circle $=r+w=(28+3.5)\ m$

$=31.5\ m$

Area of the path $=$ Area of the outer circle $-$ Area of the inner circle

$=\pi (r+w)^2-\pi r^2$

$=\frac{22}{7}\times[(31.5)^2-(28)^2]$

$=\frac{22}{7}\times(992.25-784)$

$=\frac{22}{7}\times(208.25)$

$=22\times29.75$

$=654.5\ m^2$

The area of the path is $654.5\ m^2$.

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Updated on: 10-Oct-2022

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