If the circumference of a circle increases 1m then how much the radius will be increased? And how?

Circumference, C = 1 m.

Radius = r

The relationship between the circumference

and the radius is linear, so

r = C / 2π

Subbing known values,

r = 1 / 2π

r = 0.159

The radius will be increased by 0.159 m., or 15.9 cm.

So the equation for the circumference is C= 2Pi*r. We know dC/dt=1, so we differentiate and plug in what we know:

C=2Pi*r

dC/dt=2Pi*dr/dt

1=2Pi*dr/dt

1/2Pi=dr/dt

With a radius of r1, the circumference is: ℓ1 = 2π.r1

With a radius of r2, the circumference is: ℓ2 = 2π.r2

The circumference of a circle increases 1 m: → ℓ2 = ℓ1 + 1

ℓ2 = ℓ1 + 1

2π.r2 = 2π.r1 + 1

2π.r2 - 2π.r1 = 1

2π.(r2 - r1) = 1

r2 - r1 = 1/2π

r2 = (1/2π) + r1 → the increase is (1/2π) → i.e. ≈ 0.1591 m