# What is the area of the territory located inside the ring line 70 km long?

Of course, the task implies that the ring is a circle. Well, then everything is by the formulas:

Circular length: C = 2πR

Circle area: S = πR²

And then, we express R = C/(2π)

And substitute in s = π • (C/(2π)) ²

It is required to find: S • π = π² • (C/(2π)) ²

S • π = c²/4 = 70²/4 = 4900/4 = 1225   The length of the ring branch is known – 70 km.

We need to find the area of the circle.

The area of the circle is calculated by the formula: S = ?R?.

The perimeter (length) of the circle is calculated by the formula: 2?R.

It turns out we have 2?R = 70.

?R = 70 /2 = 35.

We express from here R.

R = 35 / ?.

We substitute the value of the radius into the area formula.

S = ? (35 / ?)? = 1225 ?.

I suppose:

a) the ring line is a geometric circle,

b) the width of the ring line can be neglected.

c) I also neglect the condition for the expression of the area through s, calculating the area in km²

Because the:

C = 2πR = 70km,

That:

R = C/πR = 11.1408460165km,

And then:

S = πr² = 389.92961058km²

And why else to multiply this area by π? I don’t understand.

I would like to know the width of the ring. In the most general form, depending on the width of the ring, the area of the territory may vary from zero if the width of the ring is equal to half the radius of the ring,

2*pi*r = 70, hence R = 70/(2*pi) = 35/pi

Hence the area limited by a ring with a width of zero, (it is in the common people is circled) s = pi*35*35 = 1225*pi