Question

A circle with circumference 8, has an arc with a 288 degree central angle. What is the length of the arc?

Answer 1

Answer:
length of arc = 6.4 units

Explanation:
The length of the arc can be calculated using the following formula:
length of arc = 2π * radius * $\frac{angle}{360}$

Taking a look at the equation and comparing it with the given, we would find that:
2π*r is the equation for calculating the circumference.
We are given that the the circumference of the circle is 8 units
theta is the angle subtended by the arc = 288°

Substitute with the givens in the above equation to get the length of the arc as follows:
length of arc = 8 * $\frac{288}{360}$
length of arc = 6.4 units

Hope this helps :)

Answer 2

The length of the arc of the circle with a circumference of 8 units and the central angle of 288° is 6.4 units.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The length of the arc can be written as,

$\text{Length of the src}= \text{(Length of the circumference)} \times \dfrac{\text{Angle made at the center of the circle}}{360^o}$

Substitute the value of the circumference as 8 units, and the angle made by the arc at the centre of the circle.

$\rm \text{Length of the src}= 8 \times \dfrac{288^o}{360^o} = 6.4\ units$

Hence, the length of the arc of the circle with a circumference of 8 units and the central angle of 288° is 6.4 units.

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