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

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Area of Sector and Length of Arc
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What is a sector of a circle?

A slice formed by two radii

What is an arc?

The curved boundary of a sector

What is the formula for the area of a sector?

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

What is the formula for the length of an arc?

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

What fraction of a full circle is a 90° sector?

14\frac{1}{4}

What fraction of a full circle is a 180° sector?

12\frac{1}{2}

What does the fraction θ360°\frac{\theta}{360°} represent in sector formulas?

What portion of the full circle

For a circle with r=9r=9 cm and θ=120°\theta=120°, what is the arc length? (Use π=227\pi = \frac{22}{7})

18.86 cm

For a circle with r=9r=9 cm and θ=120°\theta=120°, what is sector area? (Use π=227\pi = \frac{22}{7})

84.86 cm²

A sector with θ=45°\theta=45° has area 77 cm². What is the radius?

14.0 cm

Which common mistake should you avoid when solving sector problems?

Rounding too early in calculations

What should you always check about the angle in sector problems?

If it's in degrees or radians

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