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.

Iam asked the question

To find the inner circumference of the circular path, we need to subtract twice the width of the path from the outer circumference.

Let's assume the radius of the pond is 'r'. The radius of the outer path would then be 'r + 2' since the path is 2 m wide.

The formula for the circumference of a circle is C = 2πr.

Given that the outer circumference of the circular path is 44 m, we can set up the equation as follows:

44 = 2π(r + 2)

Now, let's solve for 'r' to find the inner radius of the circular path:

Divide both sides of the equation by 2π:
44/(2π) = r + 2

Subtract 2 from both sides:
(44/(2π)) - 2 = r

Simplify the expression:
r ≈ (14/(π)) - 2

Now, to find the inner circumference of the path, we substitute the value of 'r' into the circumference formula:

Inner circumference = 2π(r)
Inner circumference = 2π[(14/(π)) - 2]

Simplify the expression:
Inner circumference ≈ 2(14 - 2π) m

To find the area of the path, we need to subtract the area of the pond from the area of the circular path.

The formula for the area of a circle is A = πr^2.

Let's calculate the area of the pond first:
Area of the pond = πr^2

Now, let's calculate the area of the circular path:
Area of the path = π(r + 2)^2

To find the area of the path, we subtract the area of the pond from the area of the path:

Area of the path = π(r + 2)^2 - πr^2

Simplify the expression:
Area of the path = π(r^2 + 4r + 4) - πr^2
Area of the path = 4πr + 4π - πr^2

Now, substitute the value of 'r' to find the area of the path:

Area of the path ≈ 4π[(14/(π)) - 2] + 4π - π[(14/(π)) - 2]^2

Simplify the expression:
Area of the path ≈ 4(14 - 2π) + 4π - (14 - 2π)^2

Now, calculate the value to find the exact area of the path by plugging in the value of π.

So, the inner circumference of the circular path is approximately 2(14 - 2π) m and the area of the path is approximately 4(14 - 2π) + 4π - (14 - 2π)^2.

To find the inner circumference of the circular path, we need to subtract the width of the circular path from the outer circumference.

1. Outer Circumference of the circular path = 44 m.
2. Width of the circular path = 2 m.

Inner Circumference of the circular path = Outer Circumference - Width of the circular path

Inner Circumference = 44 m - 2 m = 42 m

Therefore, the inner circumference of the circular path is 42 m.

To find the area of the path, we need to subtract the area of the inner circle from the area of the outer circle.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

To find the radius of the outer circle, we can use the formula for the circumference of a circle:
C = 2πr, where C is the circumference and r is the radius.

Outer Circumference = 44 m

Solving for r, we have:
44 = 2πr
r = 7 m (approx.)

The radius of the outer circle is 7 m.

Similarly, the radius of the inner circle will be 2 m less than the radius of the outer circle.

Inner Radius = Outer Radius - Width of the circular path
Inner Radius = 7 m - 2 m = 5 m

Now we can calculate the areas of the outer and inner circles:

Area of outer circle = π(Outer Radius)^2
= π(7 m)^2
= 49π sq m

Area of inner circle = π(Inner Radius)^2
= π(5 m)^2
= 25π sq m

Therefore, the area of the path is the difference between the area of the outer circle and the area of the inner circle:

Area of the path = Area of outer circle - Area of inner circle
= 49π - 25π
= 24π sq m

So, the area of the circular path is 24π square meters.

2 pi Ro = 44

solve for Ro
then Ri = Ro - 2
so
inner circumference = 2 pi Ri
and

Path area = pi(Ro^2-Ri^2)