Answered

The length of an arc of a circle is equal to 1/5 of

the circumference of the circle. If the length of

the arc is 2π, the radius of the circle is

Verified Answer :

length of arc    = 2π
circumference of circle =  5 . 2π  = 10π       since the arc is 1/5 of the circumference
C =2πr
r  = C/2π  =  10π/2π          = 5

The radius of the circle is 5 units.

What is a circle?

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The arc of a circle is defined as the part or segment of the circumference of a circle.

Let r be the radius of the circle.

The length of an arc of a circle = 2π

Circumference of the circle = 2πr

The length of an arc of a circle is equal to 1/5 of the circumference of the circle

⇒ \(2\pi =\frac{1}{5} 2\pi r\)

⇒ \(r=\frac{2\pi (5)}{2\pi }\)

⇒ r = 5 units

Hence we can conclude that the radius of the circle is 5 units.

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