Arc AB is One-sixth of the circumference of a circle. What is the radian measure of the central angle? StartFraction pi over 6 E

Question

1 month ago

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Arc AB is One-sixth of the circumference of a circle. What is the radian measure of the central angle? StartFraction pi over 6 E

ndFraction StartFraction pi Over 3 EndFraction StartFraction 2 pi Over 3 EndFraction StartFraction 5 pi Over 6 EndFraction

Mathematics

2 answers:

Inessa [12.5K] · Answer 1 · 2026-04-11T04:17:53+03:00

The radian representation of the central angle is π/3 radian

Further explanation

The essential formula to remember is:

Circular Area = π x R²

Circle Circumference = 2 x π x R

Where:

R = radius of the circle

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The area of the sector:

$\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}$

The length of the arc:

$\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

Now let's proceed with the problem!

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This task involves determining the central angle of the circle.

$\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

$\frac{1}{6} \times \text{Circumference of Circle} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

$\frac{1}{6} = \frac{\text{Central Angle}}{2 \pi}$

$\text{Central Angle} = \frac{1}{6} \times {2 \pi}$

$\text{Central Angle} = \frac{1}{3} \times {\pi}$

$\text{Central Angle} = \frac{1}{3}\pi \texttt{ radian}$

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Conclusion:

The radian measure of the central angle is π/3 radian

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Learn more

Calculate Angle in Triangle:
Periodic Functions and Trigonometry:
Trigonometry Formula:

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine, Cosine, Tangent, Opposite, Adjacent, Hypotenuse, Circle, Arc, Sector, Area, Central Angle, Angle

Svet_ta [12.7K] · Answer 2 · 2026-04-11T04:15:11+03:00

Svet_ta [12.7K]1 month ago

5 0

The radian measure of the central angle corresponding to an arc that is one-sixth of the circumference of a circle is StartFraction pi Over 3 EndFraction.