Question

There is a path of uniform width around a circular park. If the difference of the inner and outer boundaries of the path is 44 m. then what is the width of the path ?​

Answer 1

7m

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Answer 2

Complete step-by-step answer:
We have the radius of the outer circle as r1

We know that the circumference of a circle with radius r is given by, C=2πr

So, the circumference of the outer circle is given by,
C1=2×π×r1

Now we can consider the inner circle.
We have its radius as r2
.
Then its circumference is given by,
C2=2×π×r2

Now we can find the difference between the outer and inner circumferences.
⇒C2−C1=2×π×r2−2×π×r1

We can take the common factors outside,
⇒C2−C1=2×π×(r2−r1)
… (1)
It is given that the difference between outer and inner circumference of the circular path is 132m.
⇒C2−C1=132m
… (2)
On equating equations (1) and (2), we get,
⇒2×π×(r2−r1)=132

On rearranging, we get,
⇒(r2−r1)=132/2×π

On substituting π=22/7
, we get,
⇒(r2−r1)=132×7/2×22

On simplification, we get,
⇒(r2−r1)=21
… (3)
From the figure, the width of the path is given by subtracting the radius of the inner circle from the radius of the outer circle.
Thus from (3) the difference between their radii is, (r2−r1)=21

Therefore, the width of the path is given 21m