Question

13. A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular
path is 44 m, find the inner circumference of the circular path. Also, find area of the path.
​

Answer 1

Answer:

Let R be radius of outer circle and r be radius of inner circle.

It has been given that 44m is the circumference of outer circle,

⇒2πR=44m

⇒2×

7

22

×R=44

⇒R=

2×

7

22

44

=

2×22

7×44

=7m

It is given that circular path is 2 m wide.

So, radius of inner circle r=R−2=7−2=5 m

So, inner circumference of path =2πr=2×

7

22

×5=31.42 m

Therefore,

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

⇒π(R

2

−r

2

)

=

7

22

(7

2

−5

2

)=

7

22

×24

=75.43m

2

Answer 2

Answer:

$2\pi(r + 2) = 44 \\ r + 2 = \frac{44 \times 7}{2 \times 22} = 7$

Inner radius

$r = 5$

Outer radius

$r + 2 = 7$

Outer circle area,

= 154

Inner circle area,

= 78.57

Area of the path,

$154 - 78.57 = 75.428 \: {m}^{2}$