Area of Sector and Length of Arc (Leaving Cert Mathematics): Flashcards

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Area of Sector and Length of Arc
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Sector

Slice of circle formed by 2 radii from centre

Arc

Curved boundary forming edge of a sector

Minor arc

Shorter arc between 2 points on circle's circumference

Central angle

Angle at circle's centre between 2 radii

Area of sector formula

θ360°×πr2\frac{\theta}{360°} \times \pi r^2

Length of arc formula

θ360°×2πr\frac{\theta}{360°} \times 2\pi r

What is θ\theta in sector formulas?

Central angle in degrees

What is rr in sector formulas?

Radius of the circle

What does θ360°\frac{\theta}{360°} represent?

Fraction of complete circle the sector represents

A 90° sector is what fraction of a full circle?

14\frac{1}{4}

A 180° sector is what fraction of a full circle?

12\frac{1}{2}

Common starting fraction in both sector formulas

θ360°\frac{\theta}{360°}

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