1. Area of circular pathway

2. Area of circular pathway
Concentric circles
Circles drawn in a plane with a common centre and different radius are called
concentric circles
Area of circular pathway
A track of uniform width is laid around a circular park for walking purpose.
What is the area of this track ?
Area of the track is the area bounded between two
concentric circles.
O is the common centre of the two circles.
Let the radius of the outer circle be R and inner circle be r.

3. The shaded portion is known as the circular ring or the circular pathway. i.e. a
circular pathway is the portion bounded between two concentric circles.
width of the pathway, w = R – r units
i.e., w = R – r & R = w + r units
r = R – w units.
Area of the circular pathway = Area of outer circle – Area of inner circle
= πR – πr2 sq. units
= π (R2 – r2) sq. units
∴ Area of the circular pathway = π (R + r) (R – r) sq. units

4. larger circle is 14 cm and the smaller circle is 7 cm.
Example 1:- The adjoining figure shows two concentric circles. The radius of the
larger circle is 14 cm and the smaller circle is 7 cm.
Find the area of the circular pathway.
Solution
Given: Radius of large circle(R) = 14 m
Radius of small circle (r) = 7 m
To Find: The area of the circular pathway.
We know that Area of the circular path = π(R + r)(R – r)
14cm
7cm 3
= 22 x 3 x 7 = 462
Ans:- Area of the circular path is 462 cm2

5. Example 2:- A uniform circular path of width 2 m is laid out side a circular park of
radius 50 m. Find the cost of levelling the path at the rate of Rs 5 per m2 (Take π = 3.14)
Solution
Given: r = 50 m, w = 2 m,
We know that R = r + w = = 52 m
To Find:- Cost of levelling the path
Step1:- Find the area of circular path
Area of the circular path = π(R + r)(R – r)
= x ( ) (52 – 50) (Take π = 3.14)
= x 102 x 2
= m2
Step2:- Find the cost of levelling the circular path
The cost of levelling the path of area 1 sq m = Rs 5
The cost of levelling the path of m2 = 5 x =
Ans:- The cost of levelling the path = Rs

6. circle is 8 m, find the radius of the inner circle.
Example 3:- The area of the circular pathway is 88 m2. If the radius of the outer
circle is 8 m, find the radius of the inner circle.
Given:- Outer circle radius(R)=8m, area of the circular pathway=88 m2
To Find:- radius of inner circle
To find radius of inner circle we need to
Step1:- Find Area of outer circle
Step2:- Find Area of inner circle
Step3:- Find radius of inner circle
We know that Area of outer circle = πr2
Area of outer circle

7. Step2:- Find Area of inner circle
Area of the circular pathway = Area of outer circle – Area of inner circle
∴ Area of inner circle = Area of circular pathway – Area of outer circle
Step3:- Find radius of inner circle
We know that Area of inner circle = πr2 36
r x r =36
Since 6 x 6 = 36, ∴ r= 6
Ans:-The radius of inner circle is 6m

8. Try these
A circular well has radius 2 m. If a platform of uniform width of 1 m is laid
around it, find the area of the platform . (Take π = 3.14)
A uniform circular path of width 1.5 m is laid outside a circular park of
radius 35m. Find the cost of levelling the path at the rate of Rs 5 per m2.
(Take π = 3.14)