Fundamentals of Area and Volume (Leaving Cert Mathematics): Flashcards

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Circles and Sectors
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Definition of a circle

Shape where all edge points are equal distance from centre

Radius of a circle

Distance from centre to edge (rr)

Diameter of a circle

Distance across circle through centre

Relationship between diameter and radius

Diameter = 2imes2 imes radius

Formula for area of a circle

πr2\pi r^2

Formula for circumference of a circle

2πr2\pi r

Definition of a sector

Slice of circle between two radii and arc

Formula for area of a sector

x360×πr2\frac{x}{360} \times \pi r^2

Formula for arc length

x360×2πr\frac{x}{360} \times 2\pi r

Meaning of x360\frac{x}{360} in sector formulas

Fraction of complete circle that sector represents

Area of a semi-circle

πr22\frac{\pi r^2}{2}

Area of a quarter circle

πr24\frac{\pi r^2}{4}

Strategy for composite shapes

Break into simple parts, calculate each, add together

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