Question

Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?

Answer 1

Any smooth curve connecting two points is called an arc. The correct option is c.

What is the Length of an Arc?

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

$\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}$

where

θ is the angle, that arc creates at the centre of the circle in degree.

If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.

Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.

Hence, the correct option is c.

Learn more about the Length of an Arc:

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