The length of an arc of a circle is equal to \(\frac{1}{5}\) of the circumference of the circle. If the length of the arc is [tex]2\pi[/tex], what is the radius of the circle?

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

Answered by Poknoy | 2024-06-10

The **radius **of the **circle **is 5 units.
What is a circle?\t
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 π = 5 1 ​ 2 π r
⇒ r = 2 π 2 π ( 5 ) ​
⇒ r = 5 units
Hence we can conclude that the **radius **of the **circle **is 5 units.
Learn more about **circles **here
https://brainly.com/question/2768531
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Answered by KarpaT | 2024-06-16

The radius of the circle is 5 units, calculated by using the relationship between the arc length and the circumference. The arc length is given as 2 π , which is 5 1 ​ of the circumference. Therefore, using the formula for circumference, we find r = 5 .
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Answered by KarpaT | 2024-10-28